How would I monitor if a new entity had been saved? I am creating a module that I want to run when an entity is saved. I have used rules in the past but the overhead on the module means that I cannot use it. Is there another way that I can do this?
Thanks
If you need it to run for all entities, then your module can implement hook_entity_insert() for new entities and hook_entity_update() for changes to existing ones.

If you just need to target specific ones (node, user, etc), then most of the modules that implement entities also have insert and update hooks.