Parabolic Equations in Biology : Growth reaction movement and diffusion This book presents several fundamental questions in mathematical biology such as Turing instability pattern formation reaction diffusion systems invasion waves and Fokker Planck equations. These are classical modeling tools for mathematical biology with applications to ecology and population dynamics the neurosciences enzymatic reactions chemotaxis invasion waves etc. The book presents these aspects from a mathematical perspective with the aim of identifying those qualitative properties of the models that are relevant for biological applications. To do so it uncovers the mechanisms at work behind Turing instability pattern formation and invasion waves. This involves several mathematical tools such as stability and instability analysis blow up in finite time asymptotic methods and relative entropy properties. Given the content presented the book is well suited as a textbook for master level coursework 1.Parabolic Equations in Biology 2.Relaxation Perturbation and Entropy Methods 3.Weak Solutions of Parabolic Equations in whole Space 4.Traveling Waves 5.Spikes Spots and Pulses 6.Blow up and Extinction of Solutions 7.Linear Instability Turing Instability and Pattern Formation 8.The Fokker Planck Equation 9.From Jumps and Scattering to the Fokker Planck Equation 10.Fast Reactions and the Stefan free Boundary Problem