Learn Russian: Это центр города. - This is the centre of the city.

In Russian, the present tense of the verb "to be" is almost always skipped. So instead of saying "This is the centre", you literally just say Это центр (This the centre).

Why is the word for city written as города instead of its dictionary form город?

To say "of the city", Russian changes the ending of the noun instead of using a preposition like "of". Adding -а to the masculine word город makes it города. This form is called the Genitive case, and it is used to show belonging or connection.

The word центр is masculine. Why do we use the neuter word Это instead of the masculine Этот?

When you are introducing or pointing something out with the phrase "This is...", you always use the fixed word Это, no matter the gender of the noun. You would only use Этот if you were saying "This centre" (for example, "This centre is big").

In English we often say "city centre". Can I translate that directly and say город центр?

No, in Russian you cannot just stack two nouns together like that. You must use the "of" structure. You have to say центр города, which literally means "the centre of the city".