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The Henstock-Kurzweil integral, which is also known as the
generalized Riemann integral, arose from a slight modification of
the classical Riemann integral more than 50 years ago. This
relatively new integral is known to be equivalent to the classical
Perron integral; in particular, it includes the powerful Lebesgue
integral. This book presents an introduction of the multiple
Henstock-Kurzweil integral. Along with the classical results, this
book contains some recent developments connected with measures,
multiple integration by parts, and multiple Fourier series. The
book can be understood with a prerequisite of advanced calculus.
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