a. We use comparative adjectives to describe people and things. (e.g. This car is certainly better but it’s much more expensive.)
1. We use than when we want to compare one thing with another. (e.g. She is two years older than me.)
2. When we want to describe how something or someone changes we can use two comparatives with and. (e.g. The balloon got bigger and bigger.)
3. We often use the with comparative adjectives to show that one thing depends on another. (e.g. When you drive faster it is more dangerous -> The faster you drive, the more dangerous it is.)

b. After comparatives you can use than
1. Comparative form is ‘-er’ or ‘more ~’
2. use ‘-er’: cheap -> cheaper, thin -> thinner, pretty -> prettier (-y -> ier for two-syllable word)
3. use ‘more’ for two syllable or more: more often, use more for adverbs that end in -ly: more seriously
4. can use ‘-er’ or ‘more’ with some two-syllable adjectives: clever, narrow, quiet, shallow, simple

c. god/well -> better, bad/ badly -> worse, far -> further or farther, further also 'more' or 'additional'

a. Before comparatives we can use: much, a lot, far (= a lot), a bit, a little, slightly (= a little)
1. can use any and no + comparatives (any longer/ no longer etc.)

b. Better and better/ more and more: something changes continuously (e.g. Your English is improving. It's getting better and better)

c. The ~ the ~: the (sooner/ bigger/ more etc.) the better. The sooner the better (= as soon as possible)
1. use the ~ the ~ to say that one thing depends on another thing (e.g. The warmer the weather, the better I feel. (=if the weather is warmer, I feel better)

d. use elder (or older) when we talk about people in a family, but do not say that 'somebody is elder'

a. I don't know as many people as you do. (= you know more people)
1. It's not warm, but it isn't so cold as yesterday (= it isn't as cold as)
2. I spent less money than you (= I didn't spend as much money as you)

b. use as ~ as (but not so ~ as) in positive sentences and in questions.
1. Also twice as ~ as, three times as ~ as etc. (e.g. Our house is about three times as big as yours)

c. use the same as (not the same like). (e.g. David is the same age as James)

d. Than me/ than I am (e.g. He's not as clever as she is. = He's not as clever as her (not she)

a. Superlatives form is ‘-est’ or most: the rules are the same as those for the comparatives
1. good -> best, bad -> worst, far -> furthest/ farthest

b. normally use ‘the’ before a superlatives (the most famous etc.)

c. The superlative of old is oldest. Use eldest (or oldest) when we are talking about people in a family.

d. After superlatives we normally use in with places (e.g. What's the longest river in the world?)
1. also use ‘in’ for organisations and groups of people (e.g. Who is the youngest student in the class?)
2. For a period time, we normally use ‘of’ (e.g. What was the happiest day of your life?)
3. often use the present perfect (I have done) after a superlative. (e.g. What's the most important decision you've ever had to make?)

a. We can use comparative adverbs to show change or to make comparisons. (e.g. I forget things more often nowadays.)
1. often use 'than' with comparative adverbs (e.g. I forget things more often than I used to.)
2. We use these words and phrases as intensifiers with these patterns: much, far, a lot, quite a lot, a great deal, a good deal, a good bit, a fair bit (e.g. I forget things much more often nowadays.)
3. We use these words and phrases as mitigators: a bit, just a bit, a little, a little bit, just a little bit, slightly (e.g. She began to speak a bit more quickly.)

b. We can use superlative adverbs to make comparisons. (e.g. His ankles hurt badly, but his knees hurt worst. It rains most often at the beginning of the year.)
1. When we intensify a superlative adverb we often use the in front of the adverb, and we use these words and phrases as intensifiers: easily, much, far, by far

more about Adjective, Adverb and Adverbial