Abstarct: The scope of this thesis is to analysis geometric aspects of Lie theory of differential equations in order to study solutions and conservation laws of general non-linear heat transfer equation including its extension to fractional form‎. ‎The thesis is written in seven chapters‎. ‎The first chapter contains the basic notations and definitions of geometric concepts‎, ‎such as jet space‎, ‎prolongation‎, ‎Lie symmetries‎, ‎equivalence transformations‎, ‎etc‎. ‎Also‎, ‎some basic concepts of fractional calculus are given in this chapter‎. ‎The second chapter is devoted to studying the conservation laws‎, ‎their methods of calculations and potential symmetries‎. ‎In Chapter 3 a thorough‎ ‎analysis of the equivalence transformations‎, ‎symmetries and conservations laws of the nonlinear wave equations are presented. The generalization of the Lie group analysis to fractional partial differential equations and the computation of the conservation laws is included in Chapters 4 and 5‎. ‎In Chapter 6, ‎all discussed methods and concepts are implemented for the anisotropic nonlinear heat transfer equation‎. ‎The complete classification of admitted point symmetries is presented‎. ‎In the last part of the thesis‎, ‎we present the equivalence transformations of the time-fractional anisotropic nonlinear heat transfer equation‎. ‎Then‎, ‎a classification of symmetries and conservation laws for one and three-dimensional cases is presented‎.‎