||In the talk, we introduce the concepts and the machinery of bifurcation theory. Bifurcation theory studies the qualitative changes of the solutions for a system of equations while the control parameters of the equations vary. We will start with algebraic equations and ordinary differential equations to demonstrate basic ideas of bifurcation theory. We present different types of bifurcations including steady-state bifurcation, Hopf bifurcation and attractor bifurcation. We will conclude this talk by showing applications.