This is a excellent elementary introduction to integration using the Henstock-Kurzweil approach, at a level that should be compared with that in the book of J. D. DePree and Ch. W. Swartz [“Introduction to real analysis” (1988; Zbl 0661.26001)]. Only an elementary knowledge of real numbers is assumed and the properties of limits, continuity and differentiation are developed. The properties usually developed from the mean-value theorem of differentiation are instead deduced from elementary properties of the integral. The integral is developed as far as the theory of monotone and dominated convergence, and there is a discussion of absolute integration, Stieltjes integrals and Leader differentials [S. Leader, Am. Math. Mon. 93, 348-356 (1986; Zbl 0605.26007); Real Anal. Exch. 12(1986/87), 144-175 (1987; Zbl 0638.26009); Lect. Notes Math. 1419, 82-96 (1988; Zbl 0714.26004)]. Other forms of integration are discussed – Riemann, Moore, Darboux and a definition by sequences of partitions. The exposition is clear and straightforward; there are no exercises, and there is no index.