We undertake a comparison of observed Algol-type binaries with a library of computed Case A binary evolution tracks. The library consists of 5500 binary tracks with various values of initial primary massM₁₀, mass ratioq₀, and periodP₀, designed to sample the phase-space of Case A binaries in the range -0.10 ≤ logM₁₀ ≤ 1.7. Each binary is evolved using a standard code with the assumption that both total mass and orbital angular momentum are conserved. This code follows the evolution of both stars to the point where contact or reverse mass transfer occurs. The resulting binary tracks show a rich variety of behavior that we sort into several subclasses of case A and case B. We present the results of this classification, the final mass ratio, and the fraction of time spent in Roche Lobe overflow for each binary system. The conservative assumption under which we created this library is expected to hold for a broad range of binaries, where both components have spectra in the range G0 to B1 and luminosity classes III to V. We gather a list of relatively well-determined, observed hot Algol-type binaries meeting this criterion, as well as a list of cooler Algol-type binaries, for which we expect significant dynamo-driven mass loss and angular momentum loss. We fit each observed binary to our library of tracks using a χ²-minimizing procedure. We find that the hot Algols display overall acceptable χ², confirming the conservative assumption, while the cool Algols show much less acceptable χ², suggesting the need for more free parameters, such as mass and angular momentum loss.