BASIC is an acronym for Beginner's All-purpose Symbolic Instruction Code.
Developed by John Kemeney and Thomas Kurtz in the mid 1960s at Dartmouth
College, BASIC is one of the earliest and simplest high-level programming
languages, incorporating components of FORTRAN and ALGOL.

In 1978 Atari contracted with Shepardson Microsystems, Inc. (SMI) to create a
version of BASIC (along with a File Management System (FMS)) for the upcoming
Atari personal computers.  The following worked together on the project, which
resulted in Atari BASIC (along with the original Atari DOS):

Paul Laughton (author of Apple DOS) - project leader, co-primary contributor
Kathleen O'Brien - co-primary contributor
Bill Wilkinson - floating point scheme design
Paul Krasno - implemented the math library routines following guidelines
              supplied by Fred Ruckdeschel (author of the acclaimed text, 
              BASIC Scientific Subroutines)
Bob Shepardson - Modified IMP-16 Assembler to accept special syntax tables
                 Paul invented
Mike Peters - keypuncher/computer operator/junior programmer/troubleshooter

In late 1980/early 1981 the development rights to Atari BASIC were purchased
from Shepardson Microsystems by a new company, Optimized Systems Software
(OSS), headed by Bill Wilkinson.

Three Revisions of Atari BASIC were produced: A, B, and C:
  A - cartridge produced for use with the 400/800/1200XL (abundant)
  B - built-in to the 600XL/800XL, also produced on cartridge (rare)
  C - built-in to the 800XL(late models)/65XE/130XE/800XE/XE Game System,
      also produced on cartridge (rare)

Atari BASIC Rev. A was produced by Atari on cartridge in mass quantities 
before Shepardson Microsystems had finished debugging it.  One place these
bugs are documented is in this article by Steve Hanson from Compute! magazine,
Oct. 1981:
http://www.atarimagazines.com/compute/issue17/171_1_DOCUMENTED_ATARI_BUGS.php

When the 600XL/800XL computers were released in 1983 they included a mostly
debugged Atari BASIC Rev. B.  Unfortunately, while most existing bugs were
fixed, Rev. B introduced a new bug more serious than any of the earlier
problems.  In his article in the June 1985 issue of Compute!, Bill Wilkinson
writes:
  Each time you LOAD (or CLOAD or RUN "filename") a program, rev B adds 16
  bytes to the size of your program.  If you then save the program, the next
  time you load it in it grows by _another_ 16 bytes, and so on.
  http://www.atarimagazines.com/compute/issue61/323_1_INSIGHT_Atari.php
The problem can be alleviated by periodically, if not exclusively, using
LIST instead of SAVE or CSAVE to save your programs.

Atari BASIC Rev. C, introduced in 1984, is the final "fully debugged" version.

When running Atari BASIC, memory location 43234 ($A8E2, BASIC ROM) indicates
which Revision of BASIC is running.  At the READY prompt, enter 
"? PEEK(43234)".

If the result is:  You have Revision:       Atari Part#:
     162                  A                 CO12402+CO14502 
     96                   B                 CO60302A 
     234                  C                 CO24947A 

All 3 versions of Atari BASIC may be available for download here:
http://members.chello.nl/taf.offenga/atari_dev.htm