This document assembles 27 test problems representing a variety of examples in which least absolute deviation (or Lj^) data fitting has been used. The problems were collected from the literature, from the authors of several Lj approximation codes, and from examples encountered in practice. Optimal L]ŝ olutions to these problems (objective function value and solution vector) have been obtained using a double-precision computer code designed for checking the Kuhn-Tucker conditions and for performing an accurate reinversion of the optimal basis. . Special problem characteristics such as alternative optima, degeneracy, and rank loss are also noted. This set of test problems has proven useful in evaluating and Improving the performance of L| codes as well as in suggesting types of problem structures that might be mimicked by problem generators.