This chapter contains a brief and basic introduction to the part of the functional analysis dealing with function spaces. This chapter, as well as the next two, are aimed to serve as a “guidebook” indicating the main directions and necessary facts. As there is a large variety of sources available, and as the material of the first three chapters can be readily found in numerous monographs with much detail, we avoid giving technical proofs but restrict ourselves here to giving an exposition of main ideas, concepts, and their main properties.