I found a bunch of the books, I think the first one was The Hunt for Red October, but then I don't know what's next.
The Hunt for Red October is the fourth book in a (currently) 24-long series, known as the Jack Ryan series by Tom Clancy. That link has the books by publication date, but you might prefer them by chronological order:
Without Remorse (1970)
Patriot Games (1981)
Red Rabbit (circa spring of 1983)
The Hunt for Red October (1985)
The Cardinal of the Kremlin (1987)
Clear and Present Danger (1988)
The Sum of All Fears (1991–92)
Debt of Honor (1995–96)
Executive Orders (1996)
The Bear and the Dragon (2000)
The Teeth of the Tiger (2005, based on the age of Jack Ryan Jr.)
Clancy has other series, such as the John Clark series, which encompasses Rainbow Six and other books.