This study identifies and describes 38 branches of the haplogroup R1a STR haplotypes which currently exist in Europe or which migrated from Europe to areas in the east, south, and southeast between 6000 and 4500 years before the present (ybp). The study is based on 2471 haplotypes which have been tested for either 67-or 111-markers; it essentially creates a unified robust system, which assembles dozens of R1a-SNPs and thousands of STRs and assigned haplotypes to branches, some of which do not have SNP assignments as yet. The assembled system consists of base (deduced ancestral) haplotypes, one for each STR branch and for each SNP-assigned subclade, each with its characteristic (ancestral) set of alleles, arranged in the chronological space from ~9000 ybp to 1300 ybp. We found that the most ancient R1a subclades (R1a1-M198− and R1a1a-M198+/M417−) bearers of which currently live in Europe (the present day haplotypes are scattered between England and the Balkans) appeared in Europe at least 7300 ybp, and possibly 9000 ybp. R1a's three principal downstream subclades, L664 (North-Western branch), Z93 (South-Eastern branch), and Z283 (Eurasian branch), split from their common European ancestor at about the same time, around 7000 -6000 ybp. L664 apparently stayed in North-Western Europe; its lineage recovered and began expanding ~4575 ybp. The Z93 subclade began to expand during the Aryan migrations, on the Aryan's journey to India and the Middle East in the 3rd-2nd millennia BC. The Z283 subclade split ~5500 ybp into three branches. One of them, Z280 (the Central Eurasian branch) moved east to the Russian Plain in 4800 -4600 ybp, and formed at least 16 sub-branches there and in the course of the later westward repopulation of Europe in the 1st millennium BC-1st millennium CE. Some of the older branches, like the Russian Plain branch, largely stayed in the present Russia-Ukraine-Belarus-PolandBaltic countries region, and were described by early historians as the Scythians, Antes, Veneti, and a multitude of different proto-Slavic tribes (though many of them belonged to haplogroups other than R1a, primarily I1 and I2). Those R1a branches which are "older" than 3000 years, such as the Russian Plain branch (4600 ybp), the Western Eurasian (4300 ybp), and the Balto-Carpathian (4300 ybp), did not move en mass to Europe but stayed behind at the Russian Plain. In the middle of 1st millennium CE, the time of the collapse of the Roman Empire, multiple migrations of R1a were taking place eastward and westward; these migrations gradually formed the current landscape of R1a in Europe. All 38 branches and their datings are listed in the Appendix of this paper; current distribution maps are shown in the body of the paper.