Грамматика русского языка. Часть 12. Наречия. Глава 2. Сравнительная и превосходная степень наречий. Russian Grammar. Part 12. Adverbs. Unit 2. Comparative and Superlative Forms of Adverbs.

Adverbs, like adjectives, have comparative and superlative forms (e.g. he runs more quickly and he runs the most quickly).

(a) The comparative adverb is identical to the short form comparative adjective: so, for example: быстрее, more quickly, медленнee, more slowly, лучше, better:

Он всегда работает быстрее, чем я.
He always works more quickly thаn I do.

Adverbs ending in -и form their comparative with более:

Он всегда работает более логически, чем я.
He always works more logically than I do.

Грамматика русского языка. Часть 7. Имя прилагательное. Глава 13. Сравнительная степень: конструкции. Russian Grammar. Part 7. The Adjective. Unit 13. The Comparative. Constructions.

In English you form the second part of the comparative by using the word than (he has a more beautiful car than you). In Russian this part of the sentence is formed either by using the word чем (than) or by using the genitive.

When we are using the long form comparative in Russian, we must form the second part of the comparative by using the word чем:

У него более красивый автомобиль, чем у тебя.
He has a more beautiful car thаn you.

Грамматика русского языка. Часть 7. Имя прилагательное. Глава 12. Сравнительная степень. Продолжение. Russian Grammar. Part 7. The Adjective. Unit 12. The Comparative (Continued).

lf you are using a comparative adiective “predicatively” - i.e. after the noun it is describing (the book is more interesting), then you can use the short form comparative. This sort of comparative can only be used to mean more . . .  (interesting, beautiful etc.)

The first really important thing to remember is that you can only use the short form comparative when the person or thing you are describing is in the nominative case.

The short comparative is formed by adding the ending ee to the stem of the adjective. This ending is the same for all genders and is invariable (it never changes):

собака красивее   the dog is more beautiful
письмо интереснее   the letter is more interesting
цветы прекраснее   the flowers are more splendid

Грамматика русского языка. Часть 7. Имя прилагательное. Глава 12. Сравнительная степень. Russian Grammar. Part 7. The Adjective. Unit 12. The Comparative.

lf we say that something is “more interesting” or “less interesting”, we are using the comparative.
In English we can form the comparative by using the words more and less, or if the English adjective is very short, we can add er to the end of the adjective (it is cheaper). Russian uses the words более
(mоre) or менee (less) in front of the long form of the adjective. This is called the compound comparative.

The words более and менee never change (i.e. in their endings) but the long adjective which follows them must agree with the adjective it is describing:
This is a more (less) interesting town.
She lives in a more (less) interesting town.