The literature on random point processes and their applications has significantly increased in recent decades. However, the number of textbooks is minimal and often of a specialized nature, for example, limited to the real line or to the martingale approach for point processes. (As we will do here, we will often refer to "point processes" simply, meaning "random point processes," when no misunderstandings can arise.) We would like to offer an introduction to essential parts of the theory of marked point processes in multidimensional space for readers interested in both mathematics and applications, who possess knowledge in probability theory with its measure-theoretic and set-theoretic foundations. However, we will explain some necessary basic concepts of measure theory; for our main approach to point processes is through measure.