This book deals with analytic treatments of Markov processes. Symmetric Dirichlet forms and their associated Markov processes are important and powerful tools in the theory of Markov processes and their applications. The theory is well studied and used in various fields. In this monograph we intend to generalize the theory to non-symmetric and time dependent semi-Dirichlet forms. By this generalization we can cover the wide class of Markov processes and analytic theory which do not possess the dual Markov processes. In particular under the semi-Dirichlet form setting the stochastic calculus is not well established yet. In this monograph we intend to give an introduction to such calculus. Furthermore basic examples different from the symmetric cases are given. The text is written for graduate students but also researchers.