The Complexity of Algorithms:

1. Models of computation (old and new)
2. Upper bounds (the complexity of algorithms)
3. Lower bounds (the complexity of problems)
4. Actual complexity (input and output sensitive algorithms)
5. Expected complexity

Proving the Correctness of Algorithms:

1. Logic
2. Proof by contradiction
3. Proof by construction
4. Proof by induction
5. Existence Proofs

Linear Data Structures:

1. Arrays
2. Stacks
3. Deques
4. Linked lists
5. Adjacency matrices
6. Adjacency lists

Graphs:

1. Graph data structures:
1. Doubly-Connected-Edge-List (DCEL)
2. Winged-Edge
3. Twin-Edge
4. Quad-edge
2. Shortest paths
3. Minimal spanning trees
4. Proximity graphs
5. Hamiltonian cycles
6. Graph coloring
7. Planarity

Trees:

1. Binary trees
2. Quad trees
3. Balanced trees
4. Heaps
5. Huffman trees
6. Decision trees
7. Game trees

Divide and Conquer:

1. Sorting
2. The skyline problem
3. Convex hulls
4. Finding closest pairs

Greedy Algorithms:

1. Complexity, convexity and unimodality
2. Hill climbing algorithms
3. Quick sort
4. Quick hull

Searching Methods:

1. Maze searching
2. Binary search
1. Pure binary search
2. Binary search in a cyclic sequence
3. Binary search for a special index
4. Binary search in sequences of unknown size
5. The Bolzano method (bisection) for solving equations
6. Interpolation search
3. Depth-first search
4. Breadth-first search
5. Plane-sweep
6. Range search
7. Branch-and-bound
8. The A* algorithm

Elimination Methods:

1. Convex hulls of point sets

On-Line and Real-Time Algorithms:

1. Convex hulls of polygons
2. Convex hulls of points

Distributive Algorithms:

1. Distributive sorting
2. Bucketing methods

Prune-and-Search Algorithms:

1. Median finding
2. Ear-cutting and polygon triangulation
3. Convex hulls

Linear Programming:

1. The Simplex method
2. Megiddo's linear time algorithm

Probabilistic Algorithms:

1. Randomization
2. Randomized convex hull

1. Travelling salesman problem
2. The vertex-cover problem
3. The bin-packing problem