© 2018. The American Astronomical Society. All rights reserved. We present the first comprehensive evolutionary analysis of the rest-frame UV spectroscopic properties of star-forming galaxies at z ∼ 2-4. We match samples at different redshifts in UV luminosity and stellar mass, and perform systematic measurements of spectral features and stellar population modeling. By creating composite spectra grouped according to Lyα equivalent width (EW) and various galaxy properties, we study the evolutionary trends among Lyα, low- and high-ionization interstellar (LIS and HIS) absorption features, and integrated galaxy properties. We also examine the redshift evolution of Lyα and LIS absorption kinematics, and fine-structure emission EWs. The connections among the strengths of Lyα, LIS lines, and dust extinction are redshift independent, as is the decoupling of the Lyα and HIS line strengths, and the bulk outflow kinematics as traced by the LIS lines. Stronger Lyα emission is observed at higher redshift at fixed UV luminosity, stellar mass, SFR, and age. Much of this variation in the average Lyα strength with redshift, and the variation in Lyα strength at fixed redshift, can be explained in terms of variations in the neutral gas covering fraction and/or dust content in the ISM and CGM. However, based on the connection between Lyα and C iii] emission strengths, we additionally find evidence for variations in the intrinsic production rate of Lyα photons at the highest Lyα EWs. The challenge now is to understand the observed evolution of the neutral gas covering fraction and dust extinction within a coherent model for galaxy formation, and make robust predictions for the escape of ionizing radiation at z > 6.