Exact Controllability of a Quasi-linear heat equation with several boundary conditions is a research whose main aim is to determine the existence, uniqueness and regularity of solutions of a quasi-linear heat equation. A quasi-linear heat equation is a partial differential equation which is linear with respect to second order. I have stated the quasi-linear heat equation with the boundary conditions in a simple manner to enable one understand without much struggle. As you read through you will be able to picture how when you apply heat on a certain surface permeates/travels through from one point to another. This movement of the heat is the one we are trying to control. Before we embark on controlling we have to set the system to an initial state, this brings the element of null controllability. In null controllability, the system is taken to zero at time t=T. At this level we bring in the conditions that will enable us to drive the system to the desired state. I have used theorems, prepositions and assumptions to help us arrive at the final state. It is my hope that you will find this book very essential especially if you want to carry out research in the field p.d.e