Adaptation is driven by natural selection; however, many adaptations are caused by weak selection acting over large timescales, complicating its study. Therefore, it is rarely possible to study selection comprehensively in natural environments. The threespine stickleback (Gasterosteus aculeatus) is a well-studied model organism with a short generation time, small genome size, and many genetic and genomic tools available. Within this originally marine species, populations have recurrently adapted to freshwater all over its range. This evolution involved extensive parallelism: pre-existing alleles that adapt sticklebacks to freshwater habitats, but are also present at low frequencies in marine populations, have been recruited repeatedly. While a number of genomic regions responsible for this adaptation have been identified, the details of selection remain poorly understood. Using whole-genome resequencing, we compare pooled genomic samples from marine and freshwater populations of the White Sea basin, and identify 19 short genomic regions that are highly divergent between them, including three known inversions. 17 of these regions overlap protein-coding genes, including a number of genes with predicted functions that are relevant for adaptation to the freshwater environment. We then analyze four additional independently derived young freshwater populations of known ages, two natural and two artificially established, and use the observed shifts of allelic frequencies to estimate the strength of positive selection. Adaptation turns out to be quite rapid, indicating strong selection acting simultaneously at multiple regions of the genome, with selection coefficients of up to 0.27. High divergence between marine and freshwater genotypes, lack of reduction in polymorphism in regions responsible for adaptation, and high frequencies of freshwater alleles observed even in young freshwater populations are all consistent with rapid assembly of G. aculeatus freshwater genotypes from pre-existing genomic regions of adaptive variation, with strong selection that favors this assembly acting simultaneously at multiple loci.