My question is not how to use inner join in sql. I know about how it matches between table a and table b.
I'd like to ask how is the internal working of inner working. What algorithm it involves? What happens internally when joining multiple tables?
There are different algorithms, depending on the DB server, indexes and data order (clustered PK), whether calculated values are joined or not etc.
Have a look at a query plan, which most SQL systems can create for a query, it should give you an idea what it does.