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There are 4-kinds of fundamental option trades (long call, long put, short call, short put). And virtually any combinations up to groups to four legs can become a legitimate strategy. (Ex: Long Call + Short call can be a bull-spread, or a bear-spread, depending on what strikes you did it at). Wikipedia's Option Strategies page is a decent start: https://en.wikipedia.org/wiki/Options_strategy
For more "in depth" into some basic, conservative strategies, I suggest "The Rookie's Guide to Options", which is the book that I personally used to learn this stuff.
Its probably better to become intimately familiar with the "basic trades" (long call, short call, long put, and short put). Because at the end of the day, the more complicated strategies are just those four trades combined together.
One tidbit of "algebra" is to remember that "Long Call + Short Put == Virtual Stock". Sometimes written as Call - Put == Share. This formula really helps to break down the more complicated strategies (ie: Iron Condor which has 4 legs). It also helps you determine which strategies are roughly equivalent. (IE: Owning a share and selling a call == Share - Call is roughly equal to selling a put without owning a share.)
The Black Scholes model, aka "The Greeks", also seems important from a theoretical point of view. I've talked to some financial professionals and the pros consider Black-Scholes to be overly simplistic... but its still a model... and you need to have some basis to reality for why options have different prices. So know the model AND know the inherent weaknesses of the model (Volatility smiles and whatnot)
One last tidbit: if you are going to trade options, be sure to find a brokerage which trades multiple legs in a single unit. You don't want to pay commission on every single leg of each option strategy.
E-Trade for instance allows you to straight up buy an Iron Condor on one commission.