Learn Hardcore Russian: Цель курса — помочь тебе говорить по-русски свободно. - The course’s goal is to help you speak Russian fluently.

In Russian, a dash often links a subject (here Цель курса) with a predicate that is an infinitive phrase. It shows that the infinitive clause defines or “is” the goal. A colon would usually introduce a list or direct speech, and omitting punctuation would make the sentence harder to parse. So the dash is the standard way to connect a noun subject with an infinitive predicate.

Why is курса in the genitive case rather than nominative or another case?

Because цель is a noun that governs the genitive: you always ask цель чего? (“goal of what?”). So курс becomes курса in genitive to mean “the goal of the course.”

Why do we use the infinitive помочь instead of a finite verb like помогает?

Here помочь acts as a noun-like predicate (“to help”). The construction Цель курса — + infinitive expresses purpose or intended outcome. Using помогает would turn it into a full clause (“The course helps you…”), which is a different structure.

Why is тебе in the dative case?

Verbs like помочь require an indirect object in the dative: you help кому? (“whom?”). That’s why ты becomes тебе after помочь.

What part of speech is по-русски, and why is it hyphenated?

по-русски is an adverb of manner formed with по + dative (рУсский → русскИ). Russian adverbs with по- + adjective in dative always use a hyphen. It means “in Russian” or “Russian-ly,” i.e. “in the Russian language.”

What is свободно? Is it an adjective or adverb, and what does it modify?

свободно is an adverb meaning “freely” or “fluently.” It modifies the verb говорить, telling us how you will speak Russian.

Could we switch the order to говорить свободно по-русски or свободно говорить по-русски? Would the meaning change?

Both are grammatically correct and the basic meaning stays the same. Russian word order is relatively flexible. However, говорить по-русски свободно is very natural. Moving свободно before говорить (свободно говорить по-русски) is also common and slightly emphasizes the manner (“to speak freely in Russian”).

Can we omit тебе and say Цель курса — помочь говорить по-русски свободно?

Technically yes, but then the sentence becomes less personal or a bit vague about who is being helped. Including тебе clearly indicates the course is designed to help you specifically.

What’s an alternative way to express this idea using a subordinate clause?

You can say:
Цель курса в том, чтобы помочь тебе свободно говорить по-русски.
Here в том, чтобы introduces a subordinate purpose clause, but the meaning remains “The goal of the course is to help you speak Russian fluently.”