Volume 1, 1984 - 1993
For 62 black and white issues, running from May of 1984 to August of 1993, Volume 1 of the Teenage Mutant Ninja Turtles gave the Turtles their debut in what has always been and always will be by far the Turtles truest universethe comics.
Dreamt up one day by a napkin sketch in 1983, Kevin Eastman and Peter Laird pioneered the independent comics industry in their successful effort to get their comic creation off the ground. Printing the first issue on borrowed money, the comic quickly bore fruit, and the rest is history.
Much was varied about the first volume of TMNT. While the first twelve or so issues all seemed interconnected as part of a gritty, realistic series, Kevin Eastman & Peter Laird soon began letting others take over for them. Before too long, as guest writers and artists took their shot at the series, self-parodies of the Turtles began appearing in the series. This angered many fans and hurt sales, which led to Kevin & Peters eventual return to Volume 1 with issue #48 to its conclusion in #62.
But within some of the guest writers & artists shots at the series, between the odd balls, there were some truly unique and compelling tales. Michael Zullis take on the Turtles, for examplesweeping, larger-than-life, and with a strong emotional side. Rick McCollums stintsemotionally-driven stories with an almost spiritual side to them. Rick Veitchs "The River" arc (#24 - 26) is heralded as perhaps one of the TMNTs best ever.
Within the Kevin Eastman & Peter Laird stories lay the heart of the TMNT storyline. Their predestined conflict with Shredder and his Foot Clan, introduced in #1, resumed in the Leonardo special & #10, then concluded in the all-time classic arc (and my personal favorite) "Return to New York" (#19 - 21). This eventually led to the gigantic 13-issue "City at War" arc that concluded Volume 1, which essentially had the Turtles make peace with the Foot Clan. It was with this apparent chance for a new beginning for the TMNT that sparked the second volume that followed only a couple of months after #62.
It should also be noted that Volume 1 had its own spinoff title, Tales of the Teenage Mutant Ninja Turtles. Though it only lasted 7 issues, it had a unique feel that continued the adventures of the comic book TMNT, each issue with 1-page prologues of future Turtles reflections on past adventures (hence "Tales of the TMNT" title). Along with introducing the character Leatherhead, it also featured an appearance by Savanti Romero.
See further information about these series on the official TMNT site here.