Theory of f(R) gravity is a modification of Einstein's theory of General Relativity. It has received a great attention of the researchers due to its motivation coming from high-energy physics, cosmology and astrophysics. This theory has become a paradigm in bringing suitable cosmological models where cosmic acceleration can be achieved. In this work, two noteworthy issues of gravitational physics have been explored. One is the dark energy, thought to be responsible for the currently observed accelerated expansion of the universe while other is the gravitational collapse, a basic process driving evolution within galaxies, assembling giant molecular clouds and producing stars. Also, this book provide introduction to modern cosmology and basic knowledge about f(R) theory of gravity.