When should the spanish personal "a" be used.
Example: La semana que viene le gustaría ir a comer.
Why is the "a" before the word, "comer".
As Samdie already stated, this is not the "personal a" that you are referring to.
Here is a link to the reference article on prepositions that explains this rule in a bit more detail.
In phrases like "ir a + infinitive", or "aprender a + infinitive" it means "to" (be going to do sth, learn to do sth). English also has two kinds of infinitives: bare inf. (swim, play) and to inf. (to swim, to play). The above phrase is just an example of a verb pattern, when one verb determines the form of the following.
And your sentence means: Next week he'd like to eat out (correct me if I'm wrong).
P.S. This has nothing to do with the "personal a". It's simply a question of the use of "ir a ...".
"a" is word that gives direction to a verb. Spanish always goes in a direction and the personal "a" points the direction. "Yo le hablo" is a kind of thing that would make me thing "to who????" "Yo le hablo a el" Tells me what I need to know...I spoke to him. "Yo me fui" Pues...a donde???? "Yo me fui a mercado" Ohh....ok I see.