diff --git a/insertion_sort.py b/insertion_sort.py
new file mode 100755
index 0000000..f369757
--- /dev/null
+++ b/insertion_sort.py
@@ -0,0 +1,23 @@
+#!/usr/bin/env python3
+
+import sys
+
+def insertionsort(A):
+    # start with the first and the second
+    # insert the next element in the right place in the first elements
+    # continue until the array is done
+    for j in range(1,len(A)):
+        print(A)
+        print(A)
+        i = j - 1
+        tomove = A[j]
+        while i >= 0 and tomove < A[i]:
+            if A[i] > A[i+1]:
+                # Swap A[i] and A[j]
+                A[i+1], A[i] = A[i], A[i+1]
+            i = i - 1
+    return A
+
+
+args = [int(x) for x in sys.argv[1:]]
+print(insertionsort(args))
diff --git a/notes.md b/notes.md
index f48e18e..12b98ac 100644
--- a/notes.md
+++ b/notes.md
@@ -70,8 +70,8 @@ o(g(n)) is the family of functions O(g(n)) excluding all the functions in
 theta(g(n))
 
 ## Small omega notation
-omega(g(n)) is the family of functions Omega(g(n)) excluding all the functions in
-theta(g(n))
+omega(g(n)) is the family of functions Omega(g(n)) excluding all the functions
+in theta(g(n))
 
 ## Recap
 *asymptotically* = <=> theta(g(n))
@@ -79,3 +79,18 @@ theta(g(n))
 *asymptotically* > <=> omega(g(n))
 *asymptotically* <= <=> O(g(n))
 *asymptotically* >= <=> Omega(g(n))
+
+# Insertion sort
+
+## Complexity
+
+- *Best case:* Linear (theta(n))
+- *Worst case:* Number of swaps = 1 + 2 + ... + n-1 = (n-1)n/2 = theta(n^2)
+- *Average case:* Number of swaps half of worst case = n(n-1)/4 = theta(n^2)
+
+## Correctness
+
+Proof sort of by induction.
+
+An algorithm is correct if given an input the output satisfies the conditions
+stated. The algorithm must terminate.