In this book, an attempt has been made to present a brief study on Primordial Black Holes by assuming that gravity is described by the most attractive alternative of General Theory of Relativity and simplest type of Scalar-Tensor theory called Brans-Dicke theory. Chapter-1 contains a brief introduction to Brans-Dicke theory and some of it's cosmological applications. Chapter-2 describes the evolution of smallest type of black holes called Primordial Black Holes (PBHs). Main focus of this chapter is on the accretion of radiation by PBHs and it's impact on their evolution. Working in the setting of Brans-Dicke theory, Chapter-3 deals with a detail study on how the accretion of radiation by PBHs affects the constraints on initial mass fraction of PBHs arising from different observed astrophysical processes through their evolution. In Chapter-2 and 3, our discussion carried out by considering a stationary flow of radiation onto the PBHs. However, the real situation is much more complicated one involving non-stationary processes. So we study the non-stationary evolution of PBHs in Chapter-4 and Chapter-5. Finally, the conclusions of our study is given in Chapter-6.