Learn Russian: Дом большой, а театр маленький. - The house is big, but the theater is small.

The conjunction а is used to show a direct comparison or contrast between two different things, much like "whereas" or "while" in English. Here, we are simply contrasting the size of the house with the size of the theater. но is used for a contradiction or something unexpected (for example, "The house is big, но cheap").

Where is the word for "is" in this sentence?

In Russian, the present tense of the verb "to be" (am, is, are) is almost always left out. You just put the subject and the describing word right next to each other. So, Дом большой literally translates to "House big," but it means "The house is big."

Дом and театр are both masculine nouns. Why do the adjectives describing them end differently (-ой vs -ий)?

Both of these are standard masculine endings, but the spelling changes based on pronunciation rules. In большой, the stress falls on the very last syllable, so it takes the stressed ending -ой. In маленький, the ending is unstressed, and because of a strict Russian spelling rule (the 7-letter rule), you cannot write the letter ы after к. Therefore, it takes -ий instead of the standard unstressed -ый.

Is the comma before а required?