Learn French: Ce gymnase est pour les étudiants.

Aux is a contraction of à (to/at) and les (the plural "the"). While à can occasionally mean "for" in a few set phrases, the direct and most common translation for "for" is the preposition pour. French does not mash pour and les together into a single word, so they stay separate as pour les étudiants.

Why is it 'ce gymnase' and not 'cet gymnase'?

Gymnase is a masculine noun, so we use the standard masculine word for "this": ce. You only use cet if a masculine noun begins with a vowel or a silent 'h' (like cet ami). If the noun were feminine, you would use cette.

Do I pronounce the 's' at the end of 'les' in this sentence?

Yes, you do! Because les ends in a consonant and étudiants starts with a vowel, you must make a connection called a liaison. The usually silent 's' on les wakes up and makes a "z" sound that hooks right onto the next word. It sounds like "lay-zay-too-dee-ahn".

Does 'gymnase' mean a fitness center where I go to lift weights?