The main results achieved by the researchers of the laboratory "Group analysis of mathematical models in natural and engineering sciences", which was organized in the Ufa State Aviation Technical University, are presented in the report. During the project execution, new methods and algorithms of the modern group analysis have been developed and successfully applied for investigation mathematical models in different areas, including gas dynamics, filtration multiphase fluids in oil reservoirs, and many others. The concept of nonlinear self-adjointness, developed by the leading scientist N.H. Ibragimov, is discussed in detailed. This concept permits to construct new conservation laws for different mathematical models described by differential equations of integral and fractional orders using there's symmetries. The efficiency of this concept is demonstrated by examples. The laboratory development prospects are also presented in the final part of the report.