Learn Hardcore Russian: Сегодняшний урок короче вчерашнего. - Today’s lesson is shorter than yesterday’s.

So instead of saying Сегодняшний урок есть короче вчерашнего, Russian just says Сегодняшний урок короче вчерашнего. The is is understood from the structure: [subject] + [adjective].

What exactly does сегодняшний mean, and how is it different from сегодня?

Сегодня means today (an adverb).

Сегодняшний is an adjective derived from сегодня and means today’s / of today.

Сегодня урок. – The lesson is today.
Сегодняшний урок. – Today’s lesson.

In your sentence, Сегодняшний урок literally means today’s lesson.

What form is короче, and what is the basic adjective?

Короче is the comparative form of the adjective короткий (short).

короткий урок – a short lesson
урок короче – the lesson is shorter

So короче = shorter. It’s the standard, single-word comparative form, very common and natural.

Can I say более короткий instead of короче? Are both correct?

Yes, both are grammatically correct:

Сегодняшний урок короче вчерашнего.
Сегодняшний урок более короткий, чем вчерашний.

Differences:

Короче is shorter, more natural and preferred in everyday speech.
Более короткий is possible but sounds heavier; it’s used more when:
- there is no common short comparative, or
- you want to sound a bit more formal or precise.

With короткий, most people will prefer короче.

Why is there no word like чем to mean than before вчерашнего?

Russian has two main ways to say than in comparisons:

Using чем + nominative:
- Сегодняшний урок короче, чем вчерашний (урок).
Using the genitive case without чем:
- Сегодняшний урок короче вчерашнего (урока).

Your sentence uses the second pattern. The comparative короче is followed directly by a noun (or adjective) in the genitive, which replaces English than.

What case is вчерашнего, and why that case?

Вчерашнего is masculine singular genitive.

Reason: when a short comparative like короче, длиннее, лучше, хуже etc. is used without чем, the thing being compared to is usually put in the genitive:

Этот дом выше того дома.
Мой брат младше сестры.
Сегодняшний урок короче вчерашнего (урока).

So вчерашнего is genitive because it depends on the comparative короче in this construction.

Where did the word урок go after вчерашнего? Why is it missing?

It’s simply omitted because it’s obvious from context.

Full form would be:

Сегодняшний урок короче вчерашнего урока.

But repeating урок sounds heavy and unnecessary, so Russian usually drops the repeated noun and leaves only the adjective in the correct case:

…короче вчерашнего. – …shorter than yesterday’s (one).

This is very normal and natural.

Can I say Сегодняшний урок короче, чем вчерашний (урок)? Is that also correct?

Yes, that’s perfectly correct and very common:

Сегодняшний урок короче, чем вчерашний.

Notes:

With чем, the compared item is in the nominative: вчерашний (урок), not вчерашнего.
In writing, you normally put a comma before чем in this type of comparison.
Meaning is the same; it’s just a different grammatical pattern.

Is Сегодняшний урок короче вчерашний (without -его) correct?

No, that’s incorrect in standard Russian.

You must choose one of these patterns:

With чем + nominative:
- Сегодняшний урок короче, чем вчерашний.
Without чем + genitive:
- Сегодняшний урок короче вчерашнего.

Mixing them (no чем, but nominative вчерашний) is wrong.

Would Сегодняшний урок короче вчерашнего урока be acceptable, or is that bad style?

It is grammatically correct:

Сегодняшний урок короче вчерашнего урока.

However, in normal speech and writing, Russians usually omit the repeated noun:

Сегодняшний урок короче вчерашнего.

The version with урока sounds more formal or just a bit redundant in everyday use.

Could I say Сегодня урок короче, чем вчера instead? Does that mean the same?

Yes, and it’s also natural:

Сегодня урок короче, чем вчера.

Subtle differences:

Сегодняшний урок короче вчерашнего. – Focuses on today’s lesson vs. yesterday’s lesson as objects.
Сегодня урок короче, чем вчера. – More like Today the lesson is shorter than (it was) yesterday, emphasizing the time.

In practice, in the classroom context, they’re very close in meaning.

How flexible is the word order here? Could I say Урок сегодня короче вчерашнего?

Yes, Russian word order is quite flexible. These options are all possible, with slightly different emphasis:

Сегодняшний урок короче вчерашнего. – Neutral, very natural.
Урок сегодня короче вчерашнего. – Emphasizes today, but still natural.
Сегодня урок короче вчерашнего. – Also very common.

The most textbook-like version is the original one, but the others are acceptable in speech.