WinRAR and the RAR Archive format

RAR stands for Roshal ARchive. It is a proprietary archive file format that supports data compression, error recovery, and file spanning. It was developed by a Russian software engineer, Eugene Roshal (the first letter of his surname contributing to the name of the archive format), and is currently licensed by win.rar GmbH.
The filename extension used by RAR is .rar for the data volume set and .rev for the recovery volume set. In previous versions, if a RAR-archive was split into many smaller files (a "multi-volume archive"), the smaller files used the extensions .rar, .r00, .r01, .r02 etc.
Version 1 and 2 archive files were often used in conjunction with a parchive file archiver to create parity files for error recovery when using less-than-perfect file transmission and storage media such as newsgroups, satellite transmission, and optical discs. Version 3 has eliminated the need for third party post-processing.

Compression algorithm:
The RAR compression utility is proprietary, with a closed algorithm. RAR is owned by Alexander L. Roshal, the elder brother of Eugene Roshal. Version 3 of RAR is based on Lempel-Ziv (LZSS) and prediction by partial matching (PPM) compression, specifically the PPMd implementation of PPMII by Dmitry Shkarin.

Software:
RAR files may be created only with commercial software WinRAR, RAR, and software that has permission from the licensor Alexander Roshal (Eugene's brother). Third-party programs that can only read (unpack) RAR files include: WinZip (Windows), 7-Zip (multiplatform), Bandizip (Windows, Mac OS X), IZArc (Windows), PeaZip (Windows, Linux), Zipeg (Windows, Mac OS X), ALZip (Windows) and PowerArchiver (Windows), along with the free version of unrar (which is available for Linux and FreeBSD). Mac OS X readers include StuffIt Expander, The Unarchiver, and Zipeg. Stuffit Expander is also available for Mac OS Classic with RAR support for this platform.

WinRAR:
WinRAR is commercial software (with 40-day trial) available for Microsoft Windows. It is the only graphical tool that can write modern RAR files (RAR version 3). WinRAR's command line equivalent, RAR, is also commercial software (with 40-day trial), available for Windows, Linux, OS X, MS-DOS, OS/2, and FreeBSD. Additionally, the unrar tool from the same distributor can be used on the aforementioned platforms to extract RAR files but not to write them.
Roshal created the RAR file format and developed programs for packing and unpacking RAR files, originally for DOS in 1993, which were later ported to other platforms. The main Windows version of the archiver, known as WinRAR, is distributed as trialware, requiring payment after 40 days (although it can still be used after this period, albeit with nags). Shareware versions of this program are also available for GNU/Linux, OS X, DOS, OS/2, and FreeBSD, though they are all called simply "RAR".
RARLAB distributes the source code and binaries for a freeware command-line "unrar" program, although it is not under a free software license. This program can only decompress/extract, not create RAR files.

Other software:
There is a free software decompression library called "unrarlib", licensed under the GPL, based on an old version of unrar with permission from the author Eugene Roshal, but it can only decompress archives created by RAR versions up to 2.x. Archives created by RAR 2.9 and later (which are most RAR archives found today) use a different format which is not supported by the free library.
The paid versions of Stuffit Expander decode RAR files.
The freeware unarchiver Free RAR Extract Frog opens all types of RAR files and comes with short instructions in over 50 languages
The open source software archiver 7-Zip decompresses newer RAR files using a closed-source, free-of-charge plug-in under the "unRAR license"; the license makes the plug-in source-available but not free software.
The Unarchiver is another open source unarchiver which can decompress newer RAR files.
The free software Linux archivers File Roller, Ark, and Xarchiver can use the free UnRAR program to decompress RAR files, if they are found in the system path.

UnRAR.dll:
UnRAR.dll is a free of charge dynamic-link library (DLL) that can be downloaded from the official WinRAR site.

External Links:
Wikipedia: RAR
Wikipedia: WinRAR
WinRAR: RARLAB (Primary Homepage)

The Current Stable Release of WinRAR is:  4.20
WinRAR has versions for both Windows 32-bit (x86) and Windows 64-bit (x64) Operating Systems.

YouTube Videos:
WinRAR 4.20 Full Version For Free!! by WolfTM2008
How to Extract Multi-Part .Rar Files by idiot1579
Free Download WinRAR 4.01 Full Version by djhacksbeats
How To Get Winrar 4.0.1 Full Version For Free (32 Bit & 64 Bit) by BrilliantPCHelpHD [Note1]

Key Legend:
[Note1: This actually is shown as WinRAR version 4.01, in the program]