This paper begins by giving another formulation of the original definition of a random metric space. The present formulation is not only equivalent to the original one but also makes a random metric space automatically fall into the framework of a generalized metric space, and some new problems on topological structures are also considered. Motivated by the formulation of a random metric space mentioned above, this paper, then, explicitly presents a corresponding form of the definition of a random normed space and simplifies the definition of a random normed module. Meanwhile this paper also shows that the quotient space of an $E$-normed space is isomorphically isometric to a canonical $E$-normed space. Further, under the framework of probabilistic pseudo-normed spaces, this paper shows a probabilistic pseudo-normed linear space is a pseudo-inner product generated space iff it is isomorphically isometric to an $E$-inner product space. [This result answers an open problem recently presented by {\it C. Alsina, B. Schweizer} et al., Rend. Mat. Appl., VII. Ser. 7, No. 1, 115-127 (1997;

Zbl 0945.46012).].
Finally, based on the preceding preliminaries, this paper turns to its central part: the investigations on basic theories of random inner product spaces and random inner product modules. In this part, this paper gives a deep discussion of interesting and complicated orthogonality problems. This also further motivates us to generalize G. Stampacchiaâ€™s general projection theorem from real Hilbert spaces, in appropriate form, to real complete random inner product modules.