General resources for the related subjects that I am interested in or working on [constantly being updated]:

**Dynamical Systems**- Books
*From Calculus to Chaos by*D. Acheson*-*A very good introduction to the subject requiring very minimal background*Chaos: An Introduction to Dynamical Systems*by K. T. Alligood, T. D. Sauer, J. A. Yorke - Mathematically rigorous, step by step derivations; involves a lot of paper-pen as well as computer exercises*Introduction to Modern Dynamics*by D. D. Nolte - Very modern and original account of dynamical systems by treating up-to-date applications such as network theory, evolutionary dynamics etc..*Dynamics : Geometry of Behaviour*by R. H. Abraham and C. D. Shaw - A must read for geometric intuition of dynamical systems with full of wonderful illustrations*Chaos Book*- Original book of the MOOC Nonlinear Dynamics: Geometry of Chaos(see below)- Online Course - MOOC
*Nonlinear Dynamics: Geometry of Chaos I and II*- Absolutely wonderful resource with videos, homeworks and projects; graduate level*Nonlinear Dynamics: Mathematical and Computational Approaches*- A very good introduction MOOC for those with a minimal calculus background*Topics in Nonlinear Dynamics*- Great lectures from a great lecturer V. Balakrishnan*Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University*- Great lecture videos given by Stogatz based on his own book**Differential Equations**- Books
*Ordinary Differential Equations*by V. I. Arnold*Differential Equations and Dynamical Systems*by Lawrance Perko**Numerical Techniques & Scientific Computing****Statistical Mechanics**- Books
*Statistical Mechanics: Algorithms and Computation by*Werner Krauth - Absolutely wonderful computational statistical mechanics book which also provides the pseudocodes for all the algorithms involved*Statistical Mechanics: Entropy, Order Parameters and Complexity*by James P. Sethna - Another gem which has great exercise problems both theoretical and computational- Online Course - MOOC
*V. Balakrishnan 'Classical Mechanics' lectures series*Lecture 20-30 which covers equilbrium statistical mechanics and phase transitions*MIT OCW - Statistical Mechanics I: Statistical Mechanics of Particles*by Mehran Kerdar- Theoretical Minimum: Statistical Mechanics by L. Suskind
**Evolutionary Dynamics & Theoretical Ecology**- Books
*Evolutionary Dynamics*by M. A. Nowak*-*Standard textbook which covers the very basics of evolutionary dynamics with interesting applications*Stability and Complexity in Model Ecosystems*by Robert M. May - A classical book which defined the field of theoretical ecology from the very founder R. May - must read*Theoretical Ecology - Principles and Applications*by Robert M. May - A collection of theoretical ecology chapters written by key figures in the field; great overview for the major problems and perspectives*Evolutionary Games and Population Dynamics*by Josef Hofbauer and Karl Sigmund - Extensive treatment of Lotka-Volterra and Replicator Equations in relation with game theoretical approach to ecology and dynamical systems analysis*Models in Ecology*by John Maynard Smith - General and compact treatment of mathematical models touching key ideas of ecological modeling- Evolution and Theory of Games by John Maynard Smith - Introduction to game theoretical concepts in evolution and ecology with a lot of valuable insight
- Online Course - MOOC
- Open Yale Courses: EEB 122: Principles of Evolution, Ecology and Behavior
**Game Theory**- Online Course - MOOC
- Open Yale Courses: ECON 159: Game Theory
- Coursera - Standford Game Theory I/II
- Books
*Two-Person Game Theory*by Anatol Rapaport (Dover Pub.)*Games and Decisions*by R. D. Luce and H. Raiffa- Papers
**Mathematics related**- Books
*Mathematics Applied to Deterministic Problems in the Natural Sciences*by C. C. Lin and L. A. Segel - A very detailed and extensive collection of applied mathematical tools presented for a 'beginner' audience*Naive Set Theory*by Paul Halmos - Undergraduate beginner level set theory which provides the foundations to build up mathematical rigor in a 'naive' way