diff --git a/knapsack_library/src/algorithms_impls/FPTAS.rs b/knapsack_library/src/algorithms_impls/FPTAS.rs
new file mode 100644
index 0000000..300937b
--- /dev/null
+++ b/knapsack_library/src/algorithms_impls/FPTAS.rs
@@ -0,0 +1,70 @@
+use crate::models::knapsack::Knapsack;
+use crate::models::knapsack_solver::KnapsackSolver;
+
+/// FPTAS implementation of the Knapsack solver
+///
+/// This solver scales down the values of items to reduce precision and applies dynamic programming.
+/// The approximation factor is controlled by ε.
+/// Time complexity: O(nW/ε)
+pub struct FptasKnapsackSolver {
+    epsilon: f64,
+}
+
+impl FptasKnapsackSolver {
+    /// Creates a new FPTAS solver with the given ε value
+    ///
+    /// # Arguments
+    ///
+    /// * `epsilon` - The approximation factor (0 < ε < 1)
+    pub fn new(epsilon: f64) -> Self {
+        assert!(epsilon > 0.0 && epsilon < 1.0, "Epsilon must be between 0 and 1");
+        Self { epsilon }
+    }
+}
+
+impl KnapsackSolver for FptasKnapsackSolver {
+    fn get_name(&self) -> String {
+        format!("FPTAS (ε = {:.3})", self.epsilon)
+    }
+
+    fn solve(&self, knapsack: &Knapsack) -> Result<u64, String> {
+        let n = knapsack.get_items_len();
+        let capacity = knapsack.get_capacity();
+
+        if n == 0 || capacity == 0 {
+            return Ok(0);
+        }
+
+        // Find the maximum value among all items
+        let max_value = knapsack
+            .items
+            .iter()
+            .map(|item| item.get_value())
+            .max()
+            .unwrap_or(0);
+
+        // Scale down the values
+        let k = (self.epsilon * max_value as f64).ceil() as u64;
+        if k == 0 {
+            return Ok(0);
+        }
+
+        let scaled_items: Vec<Item> = knapsack
+            .items
+            .iter()
+            .map(|item| Item::new(item.get_weight(), item.get_value() / k))
+            .collect();
+
+        let mut dp = vec![0; (capacity + 1) as usize];
+
+        // Dynamic programming
+        for item in scaled_items {
+            for w in (item.get_weight()..=capacity).rev() {
+                dp[w as usize] = dp[w as usize].max(dp[(w - item.get_weight()) as usize] + item.get_value());
+            }
+        }
+
+        // Scale up the result
+        Ok(dp[capacity as usize] * k)
+    }
+}
\ No newline at end of file
diff --git a/knapsack_library/src/algorithms_impls/branch_Bound.rs b/knapsack_library/src/algorithms_impls/branch_Bound.rs
new file mode 100644
index 0000000..3010c48
--- /dev/null
+++ b/knapsack_library/src/algorithms_impls/branch_Bound.rs
@@ -0,0 +1,82 @@
+use crate::models::knapsack::Knapsack;
+use crate::models::knapsack_solver::KnapsackSolver;
+
+/// Branch-and-Bound implementation of the Knapsack solver
+///
+/// This solver uses recursion with pruning based on an upper bound estimate.
+/// Time complexity: Depends on the pruning efficiency, but typically much faster than brute force.
+pub struct BranchAndBoundKnapsackSolver;
+
+impl KnapsackSolver for BranchAndBoundKnapsackSolver {
+    fn get_name(&self) -> String {
+        "Branch and Bound".to_string()
+    }
+
+    fn solve(&self, knapsack: &Knapsack) -> Result<u64, String> {
+        let n = knapsack.get_items_len();
+        let capacity = knapsack.get_capacity();
+
+        if n == 0 || capacity == 0 {
+            return Ok(0);
+        }
+
+        // Sort items by value-to-weight ratio in descending order
+        let mut sorted_items = knapsack.items.clone();
+        sorted_items.sort_by(|a, b| {
+            let ratio_a = a.get_value() as f64 / a.get_weight() as f64;
+            let ratio_b = b.get_value() as f64 / b.get_weight() as f64;
+            ratio_b.partial_cmp(&ratio_a).unwrap()
+        });
+
+        let mut best_value = 0;
+        let mut current_weight = 0;
+        let mut current_value = 0;
+
+        // Recursive function to explore the tree
+        fn branch_and_bound(
+            items: &[Item],
+            index: usize,
+            capacity: u64,
+            current_weight: u64,
+            current_value: u64,
+            best_value: &mut u64,
+        ) {
+            if index >= items.len() {
+                return;
+            }
+
+            // Include the current item if it fits
+            if current_weight + items[index].get_weight() <= capacity {
+                let new_weight = current_weight + items[index].get_weight();
+                let new_value = current_value + items[index].get_value();
+                if new_value > *best_value {
+                    *best_value = new_value;
+                }
+                branch_and_bound(items, index + 1, capacity, new_weight, new_value, best_value);
+            }
+
+            // Exclude the current item
+            branch_and_bound(items, index + 1, capacity, current_weight, current_value, best_value);
+
+            // Prune using upper bound
+            let mut remaining_capacity = capacity - current_weight;
+            let mut upper_bound = current_value;
+            for i in index..items.len() {
+                if remaining_capacity >= items[i].get_weight() {
+                    upper_bound += items[i].get_value();
+                    remaining_capacity -= items[i].get_weight();
+                } else {
+                    upper_bound += (remaining_capacity as f64 * items[i].get_value() as f64 / items[i].get_weight() as f64) as u64;
+                    break;
+                }
+            }
+            if upper_bound <= *best_value {
+                return;
+            }
+        }
+
+        branch_and_bound(&sorted_items, 0, capacity, current_weight, current_value, &mut best_value);
+
+        Ok(best_value)
+    }
+}
\ No newline at end of file
diff --git a/knapsack_library/src/algorithms_impls/meet_in_the_middle.rs b/knapsack_library/src/algorithms_impls/meet_in_the_middle.rs
new file mode 100644
index 0000000..ada6f43
--- /dev/null
+++ b/knapsack_library/src/algorithms_impls/meet_in_the_middle.rs
@@ -0,0 +1,70 @@
+use crate::models::knapsack::Knapsack;
+use crate::models::knapsack_solver::KnapsackSolver;
+use std::collections::BTreeSet;
+
+/// Meet-in-the-Middle implementation of the Knapsack solver
+///
+/// This solver splits the items into two halves, generates all possible subsets for each half,
+/// and then combines the results using binary search to find the optimal solution.
+/// Time complexity: O(2^(n/2) * n)
+pub struct MeetInTheMiddleKnapsackSolver;
+
+impl KnapsackSolver for MeetInTheMiddleKnapsackSolver {
+    fn get_name(&self) -> String {
+        "Meet in the Middle".to_string()
+    }
+
+    fn solve(&self, knapsack: &Knapsack) -> Result<u64, String> {
+        let n = knapsack.get_items_len();
+        let capacity = knapsack.get_capacity();
+
+        if n == 0 || capacity == 0 {
+            return Ok(0);
+        }
+
+        // Split items into two halves
+        let mid = n / 2;
+        let (first_half, second_half) = knapsack.items.split_at(mid);
+
+        // Generate all subsets for the first half
+        let first_subsets = generate_subsets(first_half);
+
+        // Generate all subsets for the second half and sort by weight
+        let mut second_subsets = generate_subsets(second_half);
+        second_subsets.sort_by_key(|&(weight, _)| weight);
+
+        // Find the maximum value using binary search
+        let mut max_value = 0;
+        for &(weight1, value1) in &first_subsets {
+            if weight1 > capacity {
+                continue;
+            }
+            let remaining_capacity = capacity - weight1;
+
+            // Binary search for the best subset in the second half
+            let (_, value2) = match second_subsets.binary_search_by_key(&remaining_capacity, |&(w, _)| w) {
+                Ok(idx) => second_subsets[idx],
+                Err(idx) => if idx > 0 { second_subsets[idx - 1] } else { (0, 0) },
+            };
+
+            max_value = max_value.max(value1 + value2);
+        }
+
+        Ok(max_value)
+    }
+}
+
+/// Generates all possible subsets of items with their total weight and value
+fn generate_subsets(items: &[Item]) -> Vec<(u64, u64)> {
+    let mut subsets = vec![(0, 0)];
+    for item in items {
+        let mut new_subsets = Vec::new();
+        for &(weight, value) in &subsets {
+            let new_weight = weight + item.get_weight();
+            let new_value = value + item.get_value();
+            new_subsets.push((new_weight, new_value));
+        }
+        subsets.extend(new_subsets);
+    }
+    subsets
+}
\ No newline at end of file
diff --git a/knapsack_library/src/algorithms_impls/mod.rs b/knapsack_library/src/algorithms_impls/mod.rs
index ecc112a..edf703a 100644
--- a/knapsack_library/src/algorithms_impls/mod.rs
+++ b/knapsack_library/src/algorithms_impls/mod.rs
@@ -2,4 +2,7 @@ pub mod full_iteration_with_recursion;
 pub mod dynamic;
 pub mod lazy_dynamic;
 pub mod full_iteration_with_bit_mask;
-pub mod greedy;
\ No newline at end of file
+pub mod greedy;
+pub mod FPTAS;
+pub mod meet_in_the_middle;
+pub mod branch_Bound;
\ No newline at end of file
diff --git a/knapsack_library/src/algorithms_service.rs b/knapsack_library/src/algorithms_service.rs
index 6360871..66c7f93 100644
--- a/knapsack_library/src/algorithms_service.rs
+++ b/knapsack_library/src/algorithms_service.rs
@@ -25,6 +25,9 @@ impl AlgorithmsService {
             Box::new(DynamicKnapsackSolver),
             Box::new(LazyDynamicKnapsackSolver),
             Box::new(GreedyKnapsackSolver),
+            Box::new(BranchAndBoundKnapsackSolver),
+            Box::new(MeetInTheMiddleKnapsackSolver),
+            Box::new(FptasKnapsackSolver)
         ]
     }
 
diff --git a/knapsack_library/src/tests/FPTAS_tests.rs b/knapsack_library/src/tests/FPTAS_tests.rs
new file mode 100644
index 0000000..5193047
--- /dev/null
+++ b/knapsack_library/src/tests/FPTAS_tests.rs
@@ -0,0 +1,55 @@
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::models::item::Item;
+    use crate::models::knapsack::Knapsack;
+    use crate::models::knapsack_solver::KnapsackSolver;
+
+    #[test]
+    fn test_fptas_basic_case() {
+        let solver = FptasKnapsackSolver::new(0.1);
+        let items = vec![
+            Item::new(2, 3),
+            Item::new(3, 4),
+            Item::new(4, 5),
+            Item::new(5, 6),
+        ];
+        let knapsack = Knapsack::new(5, items);
+
+        let result = solver.solve(&knapsack).unwrap();
+        assert!(result >= 6 && result <= 7); // Approximation within ε
+    }
+
+    #[test]
+    fn test_fptas_zero_capacity() {
+        let solver = FptasKnapsackSolver::new(0.1);
+        let items = vec![Item::new(1, 1), Item::new(2, 2)];
+        let knapsack = Knapsack::new(0, items);
+
+        assert_eq!(solver.solve(&knapsack), Ok(0));
+    }
+
+    #[test]
+    fn test_fptas_no_items() {
+        let solver = FptasKnapsackSolver::new(0.1);
+        let items = vec![];
+        let knapsack = Knapsack::new(10, items);
+
+        assert_eq!(solver.solve(&knapsack), Ok(0));
+    }
+
+    #[test]
+    fn test_fptas_small_epsilon() {
+        let solver = FptasKnapsackSolver::new(0.01);
+        let items = vec![
+            Item::new(2, 3),
+            Item::new(3, 4),
+            Item::new(4, 5),
+            Item::new(5, 6),
+        ];
+        let knapsack = Knapsack::new(5, items);
+
+        let result = solver.solve(&knapsack).unwrap();
+        assert!(result >= 7 && result <= 7); // More precise approximation
+    }
+}
\ No newline at end of file
diff --git a/knapsack_library/src/tests/branch_Bound_tests.rs b/knapsack_library/src/tests/branch_Bound_tests.rs
new file mode 100644
index 0000000..9049107
--- /dev/null
+++ b/knapsack_library/src/tests/branch_Bound_tests.rs
@@ -0,0 +1,52 @@
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::models::item::Item;
+    use crate::models::knapsack::Knapsack;
+    use crate::models::knapsack_solver::KnapsackSolver;
+
+    #[test]
+    fn test_branch_and_bound_basic_case() {
+        let solver = BranchAndBoundKnapsackSolver;
+        let items = vec![
+            Item::new(2, 3),
+            Item::new(3, 4),
+            Item::new(4, 5),
+            Item::new(5, 6),
+        ];
+        let knapsack = Knapsack::new(5, items);
+
+        assert_eq!(solver.solve(&knapsack), Ok(7));
+    }
+
+    #[test]
+    fn test_branch_and_bound_zero_capacity() {
+        let solver = BranchAndBoundKnapsackSolver;
+        let items = vec![Item::new(1, 1), Item::new(2, 2)];
+        let knapsack = Knapsack::new(0, items);
+
+        assert_eq!(solver.solve(&knapsack), Ok(0));
+    }
+
+    #[test]
+    fn test_branch_and_bound_no_items() {
+        let solver = BranchAndBoundKnapsackSolver;
+        let items = vec![];
+        let knapsack = Knapsack::new(10, items);
+
+        assert_eq!(solver.solve(&knapsack), Ok(0));
+    }
+
+    #[test]
+    fn test_branch_and_bound_pruning_effectiveness() {
+        let solver = BranchAndBoundKnapsackSolver;
+        let items = vec![
+            Item::new(10, 60),
+            Item::new(20, 100),
+            Item::new(30, 120),
+        ];
+        let knapsack = Knapsack::new(50, items);
+
+        assert_eq!(solver.solve(&knapsack), Ok(220));
+    }
+}
\ No newline at end of file
diff --git a/knapsack_library/src/tests/meet_tests.rs b/knapsack_library/src/tests/meet_tests.rs
new file mode 100644
index 0000000..e0492a2
--- /dev/null
+++ b/knapsack_library/src/tests/meet_tests.rs
@@ -0,0 +1,39 @@
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::models::item::Item;
+    use crate::models::knapsack::Knapsack;
+    use crate::models::knapsack_solver::KnapsackSolver;
+
+    #[test]
+    fn test_meet_in_middle_basic_case() {
+        let solver = MeetInTheMiddleKnapsackSolver;
+        let items = vec![
+            Item::new(2, 3),
+            Item::new(3, 4),
+            Item::new(4, 5),
+            Item::new(5, 6),
+        ];
+        let knapsack = Knapsack::new(5, items);
+
+        assert_eq!(solver.solve(&knapsack), Ok(7));
+    }
+
+    #[test]
+    fn test_meet_in_middle_zero_capacity() {
+        let solver = MeetInTheMiddleKnapsackSolver;
+        let items = vec![Item::new(1, 1), Item::new(2, 2)];
+        let knapsack = Knapsack::new(0, items);
+
+        assert_eq!(solver.solve(&knapsack), Ok(0));
+    }
+
+    #[test]
+    fn test_meet_in_middle_no_items() {
+        let solver = MeetInTheMiddleKnapsackSolver;
+        let items = vec![];
+        let knapsack = Knapsack::new(10, items);
+
+        assert_eq!(solver.solve(&knapsack), Ok(0));
+    }
+}
\ No newline at end of file
diff --git a/knapsack_library/src/tests/mod.rs b/knapsack_library/src/tests/mod.rs
index 3f16e42..d0a1a64 100644
--- a/knapsack_library/src/tests/mod.rs
+++ b/knapsack_library/src/tests/mod.rs
@@ -3,4 +3,7 @@ pub mod dynamic_tests;
 pub mod full_iteration_with_recursion_tests;
 pub mod full_iteration_with_bit_mask_tests;
 pub mod lazy_dynamic_tests;
-pub mod greedy_tests;
\ No newline at end of file
+pub mod greedy_tests;
+pub mod branch_Bound_tests;
+pub mod meet_tests;
+pub mod FPTAS_tests;
\ No newline at end of file