Adaptation, both at the phenotypic and genetic level, is rarely observed in real time. Because of this, we often know little about the timing and dynamics of adaptation, and the underlying genetic mechanisms. Here, we use the power of experimental evolution with the yeast Saccharomyces cerevisiae and whole population sequencing to track fitness and genomic changes for 1000 asexual generations in four divergent, stressful environments. Instead of the more commonly used clonal starting conditions, we used outcrossed founder populations containing standing genetic variation. We see high parallelism within environments at the phenotypic level. In three of the four environments, replicate populations more than doubled their yield over the course of experimental evolution following a logit function: fitness increased rapidly in the first 100 generations (85% of total increase), then typically stagnated for several hundred generations before increasing again. Parallelism at the genomic level was much less pronounced, with adaptation driven by a large number of weakly selected, linked variants. Time-series pool sequencing at ten time points of population divergence and comparative genomic analyses suggest that dynamics of phenotypic change can be attributed to underlying selective sweeps. Subsequent work will focus on the fitness consequences and evolvability of hybridizing strains of yeast adapted to divergent environments, and on the analysis of single haplotype sequencing.