Blow up Theories for Semilinear Parabolic Equations 1 Introduction 2 A review of elliptic theories 3 A review of parabolic theories 4 A review of fixed point theorems. 5 Finite time Blow up for evolution equations 6 Steady State solutions 7 Blow up rate 8 Asymptotically self similar blow up solutions 9 One space variable case There is an enormous amount of work in the literature about the blow up behavior of evolution equations. It is our intention to introduce the theory by emphasizing the methods while seeking to avoid massive technical computations. To reach this goal we use the simplest equation to illustrate the methods; these methods very often apply to more general equations