There are theories on what caused the u. s.s. maine to explode while it sat in the havana harbor. what are they?

The Maine sunk because a large portion of her munitions stores (at least 5 tons) exploded. There's no real need for "theories"; that's pretty much an established fact. 

Where the theories come into it are in determining what caused the munitions stores to explode. 

The Spanish court of inquiry that examined the wreckage concluded it most likely was due to spontaneous combustion of an adjacent coal bunker. 

The US Court of inquiry concluded it was due to a mine explosion setting off the munitions stores. 

More recent investigations have gone both ways; a later US court of inquiry differed in the details from the first, while still agreeing that an external explosion was the root cause. Admiral Rickover in 1974 conducted a private investigation which ultimately largely concurred with the "coal bunker" explanation; and a 1978 analysis commissioned by the National Geographic Society concluded that the evidence was on the whole in favor of an external rather than an internal source initiating the explosion. 

Conspiracy theorists sometimes claim the US deliberately sank the Maine in order to have an excuse to go to war with Spain.