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R, also called GNU S, is an open-source language and environment designed for statistical computing and graphics. Although it's been existing for 20 years, R remains the most popular statistical programming language used today.
R is both a language as well as an environment. To access both, one needs the environment installed on its computer or server.
Today, there are 4 R environments available. The most known one is the CRAN or the original environment developed 20 years ago. All three other environments were customized by Microsoft and made available as open-source (Microsoft R Open) or as paid solution (Microsoft R Server) in the last 5 years. With its three additional environments, Microsoft aims to bring R into a professional context where one is certain of compatibility, being future-proof and scalability.
The R language is a scripting language which runs on top of an R environment (any of the four mentioned above). The R language can be written directly in the R environment or written within a console (e.g. RStudio) where the scripting is complemented with an output interface and an explorer menu. RStudio is similarly available for free.
R is generally used for statistical processing of data and thus serves as a core tool within the area of advanced analytics. Alternatives to R are Python, Scala, Matlab, SAS and many others.