Can and May

Use can to talk about ability to do something. Use may to ask for permission.

May I go to the pictures after lunch? (Here we use may because we are asking for permission.)
May I come in, Sir?
May I have another helping of the pudding?
Can you speak English? (= Are you able to speak English?)
Can you come here and hold the ladder? (= Are you able to come here and hold the ladder?)

Less and Fewer

Use less to refer to a quantity that cannot be counted. Use fewer to refer to a number than can be counted.

I am eating less rice now. (Rice is an uncountable noun.)
We found fewer apples. (Apple is a countable noun.)
They caught fewer fish. (Fish is a countable noun.)
There were fewer children than expected.
We were given less homework today than yesterday.

Lie and Lay

The verbs lie and lay are often confused.
To lie is to rest. Its forms in different tenses are given below:

Simple present: I lie
Present continuous: I am lying
Present perfect: I have lain
Simple past: I lay
Past continuous: I was lying
Past perfect: I had lain

To lie also means to not tell the truth. Its forms in different tenses are as follows:

Simple present: I lie
Present continuous: I am lying
Present perfect: I have lied
Simple past: I lied
Past continuous: I was lying
Past perfect: I had lied

To lay is to put something down. (Examples are: lay an egg, lay the table etc.) Its different forms are as follows:

Simple present: I lay
Present continuous: I am laying
Present perfect: I have laid
Simple past: I laid
Past continuous: I was laying
Past perfect: I had laid

Examples are given below:

She has lain on the bed all morning.
Alice said that she had already laid the table.
The book was laid on the chest of drawers.
I like to lie in the sun.
While lying in the bed, I got a brilliant idea.
She always lays her books neatly on the table.

Kind and Kinds

The word ‘kind’ is singular. It is used with ‘this’ or ‘that’ to modify a singular noun. The word ‘kinds’ is plural. It is used with ‘these’ or ‘those’ to modify plural nouns. Note that the same rule applies to other words such as ‘sort’, ‘type’ and ‘class’.

This kind of animal is rare. (NOT This kind of animals are rare.)
Those are the kinds of days I like. (NOT Those are the kind of days I like.)
These types of cars are very fast.