The core concept is great. Fusing monsters to create stronger or weaker ones is very cool. It can easily be expanded upon and has great potential.
At the moment the combat system is very prototype like. Once you figure out the ideal strategy (use what the enemy would have won against in the last turn) there isn't much to it. I think that type based combat would fit the game well and if you plan to expand on it please consider adding different damage types/resistances.
I didn't really understand how catching monsters works. Catching them in earlier areas worked more often than trying to catch them in later areas. (Is it dependent on the level difference between your monster and the other monster or was I just unlucky?)
What I really like about this concept is that you can either grind to get better monsters (by leveling them), or search for combinations that are stronger than your current strongest. (I don't know in how far this works in the current state of the game, but I think it's a very great idea to get rid of grinding without getting rid of grinding)
Is there any reason to have multiple monsters of the same type? Maybe catching a monster of a type you already have could somehow replace/level up the monster you already have. This would make grinding easier and not flood the monster list with useless duplicates.
It took some time for me to get used to the game. Once i got into it I started enjoying it. I'd love to see this developed further.