diff --git a/README.md b/README.md
index 109cd1ab..d464d84b 100644
--- a/README.md
+++ b/README.md
@@ -37,6 +37,8 @@ This directory contains various types of algorithm questions like Dynamic Progra
 2. [Math](algorithms/math)
 3. [Sorting](algorithms/sorting)
 4. [Greedy](algorithms/greedy)
+5. [Graph](algorithms/graph)
+6. [Backtracking](algorithms/backtracking)
 5. [Misc](algorithms/miscellaneous)
 
 ### Bookmarks
diff --git a/algorithms/backtracking/combination_sum.py b/algorithms/backtracking/combination_sum.py
new file mode 100644
index 00000000..e536945b
--- /dev/null
+++ b/algorithms/backtracking/combination_sum.py
@@ -0,0 +1,30 @@
+"""
+High Level Description:
+Given a set of candidate numbers (candidates) (without duplicates) and a target number (target), 
+find all unique combinations in candidates where the candidate numbers sums to target.
+The same repeated number may be chosen from candidates unlimited number of times.
+
+Note:
+* All numbers (including target) will be positive integers.
+* The solution set must not contain duplicate combinations.
+"""
+
+def combinationSum(candidates, target):
+    res = []
+    candidates.sort()
+    dfs(candidates, target, 0, [], res)
+    return res
+    
+def dfs(nums, target, index, path, res):
+    if target < 0:
+        return  # backtracking
+    if target == 0:
+        res.append(path)
+        return 
+    for i in range(index, len(nums)):
+        dfs(nums, target-nums[i], i, path+[nums[i]], res)
+
+'''Usage Example'''
+# candidates = [2,3,6,7]
+# target = 7
+# print(combinationSum(candidates, target))
\ No newline at end of file
diff --git a/algorithms/backtracking/combinations.py b/algorithms/backtracking/combinations.py
new file mode 100644
index 00000000..1ad9ab04
--- /dev/null
+++ b/algorithms/backtracking/combinations.py
@@ -0,0 +1,15 @@
+"""
+High Level Description:
+Given two integers n and k, return all possible combinations of k numbers out of 1 ... n.
+
+Time Complexity:
+O(2^n)
+"""
+
+def combine(n, k):
+        if k == 0:
+            return [[]]
+        return [pre + [i] for i in range(k, n+1) for pre in combine(i-1, k-1)]
+
+'''Usage Example'''
+# print(combine(5,3))
\ No newline at end of file
diff --git a/algorithms/backtracking/subset.py b/algorithms/backtracking/subset.py
new file mode 100644
index 00000000..232eea60
--- /dev/null
+++ b/algorithms/backtracking/subset.py
@@ -0,0 +1,21 @@
+"""
+High Level Description:
+Given a set of distinct integers, S, return all possible subsets.
+
+Time Complexity:
+O(2^n)
+"""
+
+def subsets(nums):
+    res = []
+    dfs(sorted(nums), 0, [], res)
+    return res
+
+def dfs(nums, start, path, res):
+    res.append(path)
+    for i in range(start, len(nums)):
+        dfs(nums, i+1, path+[nums[i]], res)
+
+'''Usage Example'''
+# S = [1, 2, 3]
+# print(subsets(S))
\ No newline at end of file