Mertens & Moore.

Chapter 1: Prologue 
Eulerian vs Hamiltonian paths on graphs.
Problems: 1.1, 1.2

Chapter 2: The Basics
2.2.3 Asymptotics, 2.2.4 Intrinsic complexity
2.4 The importance of being polynomial
Problems: 2.4, 2.12, 2.14, 2.17

Chapter 3: Insights and algorithms
3.1, 3.2 Recursion & Divide and Conquer (Sorting)
3.3 Dynamic programming
3.4 Graph searching
3.5 Greedy methods
3.8 Reductions
Problems: 3.7, 3.8, 3.11, 3.21, 3.22

Chapter 4,5
4.2.2

Chapter 10
10.3 WalkSAT

Appendix A: Mathematical tools
A.1, A.2.4