Availability is an important measure of performance for repairable systems because it can describe the probability of a repairable system being in working states. Single point and interval availability measurements (availabilities) have been widely used, but they cannot meet the requirements of all applications. In this paper, multi-point, multi-interval, and mixed multi-point-interval availabilities are introduced, which are extensions of the single point and interval availabilities. The multi-interval availability formula was given by Csenki in 2007 by using the induction method in which the multi-interval availability was called the joint interval reliability, but a new simple technique is provided to present the formula of multi-interval availability in this paper. We also consider the steady-state situations for all new availabilities. For Markov repairable systems, the calculation formulae are presented for the new availabilities, and some properties of new availabilities are discussed too. Finally, some special cases and numerical examples are given to illustrate the results obtained in the paper.