The main theme of my research is to study limit theorems in probability theory. The Large deviation principle is one of the most important limit theorems in probability theory as well as the law of large numbers and the central limit theorem. The Large deviation principle for empirical distributions was formulated in a very general framework in the 1970s. We investigate precise estimates of Laplace approximations of large deviation principle for empirical distributions of independent and identically distributed random variables and symmetric and non-symmetric Markov processes, with an aim to applications in mathematical physics. A general theory of large deviation principle and its refinement for other objects is also studied. Limit theorems related to stochastic processes in random environments are also studied.