Galaxies as the most important structures in the universe and Galaxy formation is a sequential redistribution process.The basic picture of galaxy formation was first proposed by White and Rees.The physical processes involved in galaxy formation are very numerous and complex. We know very little about most of these processes. Therefore, we can only describe them with a few empirical formulas. In this article the popular simulation techniques for galaxy formation are discussed in detail, based on the most recently observed cosmic star formation history. This study will focus mostly on the goals of galaxy development by describing the processes of star formation, gas dispersion, dark matter, and galaxy correlation. In this paper, we do not study the formation process of a specific galaxy, but focus on the formation process of a large sample of galaxies in the framework of the whole cosmology We are also concerned not with the specific properties of a particular galaxy, but with the statistical properties of the whole sample of galaxies.Therefore the paper will next explore hydrodynamic techniques such as N-body simulation, other modified f (R) gravity models, smoothed-particle hydrodynamic simulation, and semi-analytic models to mimic the process of galaxy formation. This article finishes with a summary of galaxy formation.