Bose Einstein Condensate (BEC) is the fifth state of matter in condensed matter physics. It is the most impressive example of quantum behaviour on a macroscopic scale but the most difficult state to observe. When low-density boson gas is cooled to a temperature nearly absolute zero, then BEC is formed. In this condition, the bosons have almost no free energy to move relative to each other. They clump together, come into the lowest quantum state, and behave as a single atom. Then microscopic quantum mechanical phenomena work on a macroscopic scale. This chapter summarizes the history and the developments regarding BEC with a brief discussion of the key scientists in this field. In the next section, the summary of the all chapters is given

An electron and an electron hole are attracted to each other by electrostatic Coulomb force and combine. This bound state of electron-hole pair is known as an exciton. It can carry energy without transferring net electric charge because it is an electrically neutral quasiparticle. Excitons exist in semiconductors, insulators and some liquids. Frenkel exciton and Wannier-Mott exciton are the two types of excitons. In this section, the origin of excitons, types of excitons, and the relaxation and thermalization behavior of excitons with some research results have been discussed.

Polariton is a bosonic quasiparticle. When an electromagnetic wave strongly interacts with the dipole active transition of the medium, then polariton is formed [1]. In other words, when light scatters and goes through any interrelated resonance, then the polaritons can be formed. In this chapter, the history of polariton, category of polaritons, their constituents, and light-matter interaction have been explained. Special condensate behaviour of polaritons like polariton lasing, superfluidity, and quantized vortices are also explained.

The research on the Bose Einstein Condensation (BEC) of polaritons is of increasing importance due to its many technological applications. Several experimental and theoretical methods have been applied for the investigation on the BEC of excitons. Different experimental procedures and theoretical methods have been discussed in this chapter. Current research progress in this field and the applications of the BEC are also explained. 

Several experimental and theoretical procedures have been used to get the Bose Einstein Condensation (BEC) of polaritons. Nowadays, the investigation of the BEC of polaritons is vastly popular and increasing attention in atomic as well as solid-state physics because it has many technological applications. In this chapter, different experimental procedures, excitation, and observation methods are explained. Recent research developments in this field and the application of the BEC also are discussed.