This study identifies and describes 38 branches of STR haplotypes of the R1a haplogroup that currently exist in Europe or that migrated from Europe to areas in the east, south and southeast between 6,000 and 4,500 years ago (bp years). The study is based on 2471 haplotypes that have been tested for 67 or 111 markers; it essentially creates a unified, robust system that combines dozens of R1a SNPs and thousands of STRs and assigns haplotypes to branches, some of which do not yet have SNPs assigned. The assembled system consists of basic (deduced ancestral) haplotypes, one for each STR branch and for each subclade with an assigned SNP, each with a characteristic (ancestral) set of alleles, ordered in chronological space from ~9000 years bp to 1300 years bp. We discovered that the oldest R1a subclades (R1a1-M198- and R1a1a-M198+/M417-), whose carriers are currently living in Europe (the current haplotypes are scattered between England and the Balkans), appeared in Europe at least 7300 years ago, and probably 9000 years ago. The three major subclades of R1a, L664 (Northwestern branch), Z93 (Southeastern branch) and Z283 (Eurasian branch), split from a common European ancestor at about the same time, about 7000-6000 years ago. L664 apparently remained in northwestern Europe; its lineage re-emerged and began expanding about 4575 years ago. The Z93 subclade began to develop during the migration of the Aryans, during their travels to India and the Middle East in the 3rd-2nd millennia BC. Subclade Z283 split around 5500 BC into three branches. One of them, Z280 (the Central Eurasian branch), moved eastward into the Russian Plain between 4800-4600 BCE, where it formed at least 16 branches, as well as during the subsequent westward repopulation of Europe in the 1st millennium BCE. - 1st millennium AD. Some of the older branches, such as the Russian Lowland branch, have largely remained in the present-day region of Russia, Ukraine, Belarus, Poland and the Baltics, and were described by early historians as Scythians, Antes, Venedians and a variety of different Proto-Slavic tribes (although many of them belonged to haplogroups other than R1a, mainly I1 and I2). Those branches of R1a that are "older" than 3,000 years, such as the Russian Plain branch (4,600 BCE), the West Eurasian branch (4,300 BCE) and the Baltokarp branch (4,300 BCE), did not move en masse to Europe, but remained in the Russian Plain. In the middle of the 1st millennium AD, during the collapse of the Roman Empire, there were numerous R1a migrations to the east and west; these migrations gradually shaped the current R1a landscape in Europe. All 38 branches and their dating are listed in the appendix to this article; current distribution maps are included in the body of the article.