  This text grew out of notes I have used in teaching a one quarter course on
integration at the advanced undergraduate level. My intent is to introduce the
Lebesgue integral in a quick, and hopefully painless, way and then go on to
investigate the standard convergence theorems and a brief introduction to the
Hilbert space of $L^2$ functions on the interval.
  The actual construction of Lebesgue measure and proofs of its key properties
are relegated to an appendix. Instead the text introduces Lebesgue measure as a
generalization of the concept of length and motivates its key properties:
monotonicity, countable additivity, and translation invariance.
