Learn Hardcore Russian: В нашем классе много студентов. - There are many students in our classroom.

In this sentence, в нашем классе means in our class.
After в, when you talk about a location (where something is), Russian normally uses the prepositional case (here: классе).

Compare:

в классе – in the class / in the classroom (location)
в класс – into the class / into the classroom (movement, direction)

Why is it нашем and not наш or something else?

Нашем is the prepositional case form of the possessive adjective наш (our).

Наш changes its ending to agree with the noun it describes:

Masculine / neuter, prepositional singular ending is -ем:
- наш дом → в нашем доме (in our house)
- наш класс → в нашем классе (in our class)

Since класс is masculine singular and here is in the prepositional case (because of в + location), наш must also be masculine singular, prepositional: в нашем классе.

What case is классе, and when do we use that form?

Классе is in the prepositional case.

You use the prepositional case mainly:

After certain prepositions (like в, на, о/об)
To talk about location (where?) or topic (about what?)

Here в классе answers the question где? (where?) → в классе (in the class).
So: класс (nominative) → в классе (prepositional).

Why is it классе with -е at the end instead of just класс?

The base form is класс (nominative). To form the prepositional case for most masculine nouns ending in a consonant, you add -е:

город → в городе (in the city)
магазин → в магазине (in the store)
класс → в классе (in the class)

So -е is simply the regular prepositional ending: класс → классе.

The double с is part of the stem класс, not added by the case ending.

What does много mean, and how does it work in this sentence?

Много means a lot (of), many, much.

In this sentence:

много студентов = a lot of students / many students

Important grammar point:
Words like много (a lot of), мало (few/little), несколько (several) usually require the genitive case after them:

много студентов (a lot of students)
мало времени (little time)
несколько книг (several books)

So много controls the case of the following noun: it forces студентов to be genitive plural.

Why is it студентов and not студенты?

Студентов is the genitive plural of студент (student).

Normal plural (nominative):

студент → студенты – students

Genitive plural:

студент → студентов – (of) students

After много, Russian uses the genitive, not the nominative.
So you cannot say много студенты; it must be много студентов.

This pattern is very common:

много людей (a lot of people)
много машин (many cars)
много студентов (many students)

What is the difference between много студентов and многие студенты?

They look similar but are used differently.

много студентов
- Literally: a lot of students / many students (quantity)
- много is a quantity word that takes genitive plural: студентов.
- Used for neutral statements about how many there are.
- Example:
  - В нашем классе много студентов. – There are many students in our class.
многие студенты
- Literally: many (of the) students (a subset of some known group)
- многие is a plural adjective (like many) and takes nominative plural: студенты.
- Usually acts as the subject doing something:
  - Многие студенты опоздали. – Many (of the) students were late.

In your sentence:

В нашем классе много студентов. – correct, means the class is large.
В нашем классе многие студенты. – incomplete/strange; you’d expect a verb:
- В нашем классе многие студенты работают. – In our class, many students work (have a job).

Why is there no word meaning are (like are in There are many students in our class)?

Russian often omits the verb “to be” in the present tense when simply stating what something is or that something exists.

English:

There are many students in our class.

Russian allows:

В нашем классе много студентов. (no verb)

You could say есть (“there is/are”), but here it’s usually unnecessary and can sound a bit heavier or more emphatic:

В нашем классе есть много студентов. – There are many students in our class (emphasizing existence; stylistically less common in this exact phrase).

So the natural version is without a present-tense to be.

Does много agree in gender/number with студентов?

No, много is indeclinable – it does not change its form for gender, number, or case.

It’s always много:
- много студентов (many students)
- много девушек (many girls)
- много времени (a lot of time)
- много воды (a lot of water)

What does change is the noun after it, which goes into the genitive:

masc. студент → студентов
fem. девушка → девушек
neut. время → времени
fem. uncountable вода → воды

Does класс here mean the classroom or the group of students (a class)?

Usually, in this kind of sentence, класс means the group of students, i.e. a school class or a cohort:

В нашем классе много студентов.
→ Our class (group) has many students. / There are many students in our class.

If you want to be clearly talking about the room, Russian more often uses something like:

В нашем кабинете много студентов. – There are many students in our classroom (in our room).
В нашей аудитории много студентов. – There are many students in our lecture hall.

Context decides, but in isolation, learners are usually taught to understand this as “our class (group) has many students.”

Can I change the word order? For example: Много студентов в нашем классе or В нашем классе студентов много?

Yes, Russian allows flexible word order, and all of these are grammatically correct, but they differ in emphasis:

В нашем классе много студентов.
- Neutral, most typical.
- Focus is slightly on how many students there are (many).
Много студентов в нашем классе.
- Puts много студентов at the beginning, emphasizing the large number.
- Feels like: It’s our class that has many students (as opposed to others).
В нашем классе студентов много.
- Fronts в нашем классе, then moves студентов before много.
- Often used to stress the contrast:
  - В нашем классе студентов много, а в вашем — мало.
    In our class there are many students, and in yours, few.

All are understandable; the first one is the safest and most neutral.

What is the difference between в классе and в класс?

The difference is location vs direction:

в классе – in the class / in the classroom (where?)
- Uses prepositional case: классе
- В нашем классе много студентов. – There are many students in our class.
в класс – into the class / into the classroom (where to? into where?)
- Uses accusative case: класс (same form as nominative here)
- Я захожу в класс. – I am going into the classroom.

So:

в классе = inside (static location)
в класс = (movement) into

How is the sentence stressed and roughly pronounced?

Stress (accent marks added):

В на́шем кла́ссе мно́го студе́нтов.

Stressed syllables:

на́шем – stress on на
кла́ссе – stress on клас
мно́го – stress on мно
студе́нтов – stress on де

Rough pronunciation (English-style approximation):

В на́шем – [v NAH-shem]
кла́ссе – [KLAH-ssye]
мно́го – [MNOH-ga] (the initial мн is pronounced together, like mn in English “mnemonic”)
студе́нтов – [stoo-DYEN-taf] (final в is devoiced to [f] in normal Russian speech)

So altogether:
[v NAH-shem KLAH-ssye MNOH-ga stoo-DYEN-taf]