A Guild to the Literature

Point-Set Topology

Willard, General Topology
Munkres, Topology

Algebraic Topology

Munkres, Elements of Algebraic Topology
Hatcher, Algebraic Topology
Bredon, Topology and Geometry
Massey, A basic course in algebraic topology

Differential Topology

Hirsh, Differential Topology
Guillemin & Pollack,Differential Topology
Manfredo P. do Carmo, Riemannian Geometry

Manifolds

Jeff Lee, Manifolds and Differential Geometry
John Lee, Introduction to Topological Manifolds 
          Introduction to Smooth Manifolds 
          Riemannian Manifolds: An Introduction to Curvature  
Moise, Geometric Topology in Dimensions 2 and 3
Hempel, 3-Manifolds
Jaco, Lectures on Three-Manifold Topology
Saveliev, Lectures on the Topology of 3-Manifolds
Morgan, The Poincare conjecture. 
        International Congress of Mathematicians. 
        Vol. I, 713-736, Eur. Math. Soc., 2007. 
Scott, The geometries of 3-manifolds.
       Bull. London Math. Soc. 15 (1983), no. 5, 401-487. 
Thurston, The Geometry and Topology of Three-Manifolds
          http://www.youtube.com/watch?v=4jdmkUQDWtQ

Knot Theory

Gilbert & Porter, Knots and Surfaces
Rolfsen, Knots and Links
Burde & Ziechang, Knots
Adams, The Knot Book

Dynamical Systems

Devaney, An Introduction to Chaotic Dynamical Systems
Robinson, Dynamical Systems: Stability, Symbolic Dynamics, and Chaos
Robinson, An Introduction to Dynamical Systems: Continuous and Discrete 
Hirsh, Differential Equations, Dynamical Systems, and an Introduction to Chaos
Katok, Modern Theory of Dynamical Systems
Aligood, Sauer & Yorke, Chaos: An Introduction to Dynamical Systems 
Guckenheimer & Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields 
Franks, Homology and Dynamical Systems 
Shub, Global Stability and Dynamical Systems
Palis &  de Melo, Geometric Theory of Dynamical Systems

Symbolic Dynamics

Marcus & Lind,An Introduction to Symbolic Dynamics and Coding
Kitchens, Symbolic Dynamics

Knots in Dynamical Systems

Ghrist, Holmes & Sullivan, Knots and Links in Three-Dimensional Flows