Learn Hardcore Russian: Этот урок более сложный, чем прошлый. - This lesson is more difficult than the last one.

Synthetic (single-word) comparative
- сложный → сложнее (more difficult)
Analytic (two-word) comparative
- сложный → более сложный (literally: more complex/difficult)

Both Этот урок сложнее, чем прошлый and Этот урок более сложный, чем прошлый are correct and natural.

The difference is mostly stylistic:

сложнее is shorter and very common in everyday speech.
более сложный is a bit more formal or careful, and often used in writing or when you want to sound slightly more precise or neutral.

Is there any real difference in meaning between более сложный and сложнее in this sentence?

In this exact sentence, there is no real difference in meaning. Both say:

This lesson is more difficult than the previous one.

Subtle tendencies:

сложнее: very typical in spoken Russian; also fine in writing.
более сложный: slightly more formal, can sound a bit more “measured” or “academic”.

You could choose either without changing the basic message.

Why is it сложный, not сложно?

Because сложный is an adjective agreeing with the noun урок.

Этот урок сложный. – This lesson is difficult.
Here сложный describes the lesson (a thing), so it must be an adjective: masculine, singular, nominative.

The adverb сложно is used with verbs, not nouns:

Учиться сложно. – It is hard to study.
Решить эту задачу сложно. – It is difficult to solve this problem.

In your sentence, we are not saying “it is difficult to do X”; we are describing the lesson itself, so we need сложный, not сложно.

Both сложный and прошлый end in -ый. Why do they have that form?

They are both adjectives describing урок and must agree with it in:

gender: masculine
number: singular
case: nominative

So they take the ending -ый:

урок (m.sg.nom.)
- этот урок
- сложный урок
- прошлый урок

In the sentence:

Этот урок – subject in nominative.
(есть) более сложный – predicate adjective in nominative, agreeing with урок.
чем прошлый – short for чем прошлый (урок); again masculine singular nominative.

Why can we just say чем прошлый and not чем прошлый урок?

This is a common case of ellipsis (leaving out words that are obvious from context).

The full, “complete” version would be:

Этот урок более сложный, чем прошлый урок.

Since урок is already mentioned right before, Russian usually drops the repeated noun:

Этот урок более сложный, чем прошлый.

Native speakers do this all the time when the meaning is still perfectly clear.

Could we also say Этот урок сложнее прошлого or Этот урок сложнее прошлого урока?

Yes, both are grammatical and natural:

Этот урок сложнее прошлого.
Этот урок сложнее прошлого урока.

This uses a genitive instead of чем for comparison.

Comparison patterns:

With чем:
- Этот урок сложнее, чем прошлый.
With genitive:
- Этот урок сложнее прошлого (урока).

Meaning is basically the same. Notes:

The чем pattern is slightly more neutral and very common.
The genitive pattern is also standard, maybe a bit more typical in written language.
With some adjectives/contexts, one pattern may feel more idiomatic than the other, but here both are fine.

Can we change the word order and say Этот более сложный урок? Does that mean the same thing?

Этот более сложный урок is possible, but it has a different focus.

Этот урок более сложный, чем прошлый.
- Neutral statement about this particular lesson:
  This lesson is more difficult than the previous one.
Этот более сложный урок…
- This sounds like you are choosing or contrasting this lesson among several:
  This more difficult lesson… (as opposed to some other, easier lesson)

So:

Этот урок более сложный – main information is about how difficult this lesson is.
Этот более сложный урок – main information is that this one is the more difficult lesson in some set.

Is the comma before чем always necessary here?

In this sentence, yes, the comma is standard:

Этот урок более сложный, чем прошлый.

Reason: чем functions as a conjunction introducing a comparative clause (elliptical: чем был прошлый урок). Before such a чем-clause, Russian normally puts a comma.

You do not put a comma when чем acts as a particle in set patterns like:

более чем странно – more than strange (no comma)

But in your sentence, it is a normal comparison with чем, so use the comma.

Why is it этот, not это or эта?

The form of этот must agree with the noun it modifies:

этот – masculine singular (for урок, стол, день)
эта – feminine singular (for тема, книга, ночь)
это – neuter singular (for задание, слово, место)
эти – plural for all genders (for уроки, книги, слова)

Since урок is masculine singular, the correct form is этот:

Этот урок более сложный, чем прошлый.

How would the sentence change with a feminine or a plural noun?

Adjust all the words to agree with gender and number.

Feminine noun, e.g. тема (topic):

Эта тема более сложная, чем прошлая.
(эта / сложная / прошлая – feminine singular)

Neuter noun, e.g. задание (task):

Это задание более сложное, чем прошлое.

Plural noun, e.g. уроки (lessons):

Эти уроки более сложные, чем прошлые.

The structure stays the same; only endings and demonstratives change.

Why use the long form сложный instead of the short form сложен?

Russian has long and short adjective forms:

long: сложный
short: сложен

Basic difference:

Long forms (сложный) – more descriptive, neutral, can be both attributive and predicative:
- сложный урок, урок сложный
Short forms (сложен) – mostly predicative, often sound a bit more formal or emphasize a state/result:
- урок сложен для новичков – the lesson is difficult for beginners

In comparisons, the long form is more common:

Этот урок более сложный, чем прошлый. – most natural.
Этот урок более сложен, чем прошлый. – also possible, but sounds more formal/bookish.

For everyday speech and standard usage, более сложный is the default choice.

What is the difference between прошлый, предыдущий, and последний? Could we use them all here?

They are related but not identical:

прошлый
- Literally: the last one / the one before now
- Typical in sequences like lessons, weeks, years:
  - прошлый урок – the previous lesson
  - в прошлую неделю – last week
предыдущий
- Literally: the preceding one
- Slightly more formal, often in written or technical contexts:
  - предыдущий пункт, предыдущая глава
последний
- Usually: the last (final) one
- Can be ambiguous between previous and final, but modern usage tends to interpret it as final:
  - последний урок – usually means “the final lesson”, not just “the previous one”

In your sentence, the most natural are:

Этот урок более сложный, чем прошлый. – very normal.
Этот урок более сложный, чем предыдущий. – also correct, a bit more formal.

Using последний here would normally sound like you mean the final lesson, not just the one before this one, so it is not a good choice.

How do you pronounce the whole sentence? Where is the stress?

Stress pattern (stressed syllables in CAPS; ё is always stressed):

Э́тот уРОК бо́лее СЛОЖный, чем ПРОшлый.

Rough phonetic approximation:

Э́тот – [É-tat]
урок – [u-ROK]
бо́лее – [BO-lee-ye]
сло́жный – [SLOZH-nyy] (zh like the s in measure)
чем – [chem] (like chem in chemistry)
про́шлый – [PROSH-lyy] (sh + soft l)

Natural speech will connect words smoothly:
[É-tat u-ROK BO-lee-ye SLOZH-nyy, chem PROSH-lyy].

Is урок the only word for “lesson” or “class”? Could we replace it here?

Russian has several common words in this area:

урок
- Lesson (especially at school); also a particular unit in a textbook.
- Этот урок более сложный, чем прошлый. – very natural.
занятие
- A class or session of study/activity (broader); often used for university classes, courses, clubs.
- Это занятие более сложное, чем прошлое.
лекция
- A lecture (one person talking, often at university).
- Эта лекция более сложная, чем прошлая.

All three can fit the same grammar pattern; you just change the gender and endings accordingly.