The verb pair приглашать/пригласить means ‘to invite.’ Note the с~ш alternation in the perfective:

The person you invite goes in the accusative case:

The place you invite someone to appears in a motion phrase, so you often have в/на followed by the accusative case:

You can also use к + dative to specify the person one is going to visit, which more often than not is specified with к себе or к нам, and в гости is often included as well:

It's possible to get names after к as well:

¹ Савик Шустер is the host of «Шустер live», a Ukrainian socio-political talk show. Despite being broadcast on Ukrainian TV, the show is conducted in Russian.

Они is a pronoun that replaces grammatically plural nouns. It declines like this:

The primary meaning of они is they/them in its various forms. In such contexts you get sentences like:

But the interesting part of this word is when it refers to plurale tantum nouns. Such nouns are ones that grammatically occur in the plural only, never in the singular. Sometimes a noun is plurale tantum in both Russian and English, like брюки pants. If они is referring to such a word, then its forms are simply translated as they/them:

Sometimes a noun is plurale tantum in Russian, but singulare tantum (singular only) in English, such as деньги money. When они refers to such a word, then its forms are simply translated as it:

English and Russian both have special comparison forms for adjectives and adverbs, which makes them seem sort of similar. In English the comparative form often ends in -er, and in Russian it often ends in -е or -ее:

But here is a curious thing: if you want to say how many times someone or something is faster, richer, taller or older, then in English there are two constructions you can use. One of them uses an “as...as” phrase without a comparative form, and one of them uses a comparative form with a ‘than’ phrase.

In Russian you always use the comparative form. The word for ‘time’ in this context is раз, which has an irregular genitive plural ‘раз’, and the number must be preceded by the preposition в, which in this context works with the accusative case of the number:

Oh, let's try a few more.

¹ If you look at the Wikipedia article on Joan Collins, you will see her name transliterated as Джоан Коллинз, which has an unpronounced ‘а’ and an unpronounced extra ‘л’, which have been added under the influence of English spelling. That is a *bad thing*. Dear Russian Wikipedia authors, please do not fall under the terrible influence of English spelling. You have a marvelous tradition in Russian of spelling things much more closely to their pronunciation. It is why the Russian application of Cyrillic is superior to the English application of the Latin alphabet. Notice that the author of the Kira Knightley article didn't make that mistake. Please maintain your excellent and sensible tradition, and, eight hundred years from now, when we English speakers finally have a sensible spelling reform, you can taunt us with an alphabetic “I told you so!”

In English when you want to say how often something happens and the period over which it occurs, you can use two constructions. The first uses no preposition, and the second uses the preposition ‘per’:

In English the ‘per’ version sounds more formal and stilted, and the prepositionless version sounds normal. In Russian the prepositionless version is not an option; you must use the preposition в:

At first glance it might seem that год is in the nominative case, but that is because it is a masculine inanimate noun. If we see a feminine noun in that context it is clearly accusative:

If you want to ask how often something happens, then the phrase to use is как часто:

That last example is interesting because you could rephrase it with minutes and skip the preposition:

Note the interesting use of the plural form of каждый before a number greater than one.

The word мы means we. It declines like this:

I often encounter the word in sentences like this: