Other, others, the other or another?

(From English Grammar Today - https://dictionary.cambridge.org/grammar/british-grammar/other-others)

Other

Other means ‘additional or extra’, or ‘alternative’, or ‘different types of’.
 

Other as a determiner
We can use other with singular uncountable nouns and with plural nouns:

* The embassy website has general information about visas. Other travel information can be obtained
by calling the freephone number. (additional or extra information)
* Some music calms people; other music has the opposite effect. (different types of music)
* What other books by Charles Dickens have you read, apart from ‘Oliver Twist’? (additional or extra
books)
* This one’s too big. Do you have it in other sizes? (alternative sizes)

If we use other before a singular countable noun, we must use another determiner before it:

* I don’t like the red one. I prefer the other colour.
Not: I prefer other colour.
* Jeremy is at university; our other son is still at school.
* He got 100% in the final examination. No other student has ever achieved that.
* There’s one other thing we need to discuss before we finish.
 

Warning:
Other as a determiner does not have a plural form:
* Mandy and Charlotte stayed behind. The other girls went home.

Not: The others girls …

Other as a pronoun
We can use other as a pronoun. As a pronoun, other has a plural form, others:
* We have to solve this problem, more than any other, today.
* I’ll attach two photos to this email and I’ll send others tomorrow. 

The other

The other as a determiner
The other with a singular noun means the second of two things or people, or the opposite of a set of
two:
*This computer here is new. The other computer is about five years old.
* A: D’you know the Indian restaurant in Palmer Street?
B: Yes
A: Well, the gift shop is on the other side of the street, directly opposite. (the opposite side)

The other with a plural noun means the remaining people or things in a group or set:
* Joel and Karen are here, but where are the other kids? (the remaining people in a group)
* Where are the other two dinner plates? I can only find four. (the remaining things in a set – here six
plates)

The other as a pronoun

We can use the other as a pronoun, especially to refer back to something which has been mentioned already in the sentence:

* He had his hat in one hand and a bunch of flowers in the other.
* She has two kittens, one is black and the other is all white.

Another

When we use the indefinite article an before other, we write it as one word: another. Another means ‘one
more’ or ‘an additional or extra’, or ‘an alternative or different’.

Another as a determiner
We use another with singular nouns:

* Would you like another cup of coffee?
* You’ve met Linda, but I have another sister who you haven’t met, called Margaret.
* I don’t like this place. Is there another café around here we could go to? (alternative or different)

Another as a pronoun
We can use another as a pronoun:

* The applications are examined by one committee, then passed on to another.

Other, others, the other or another: typical errors

When other is a determiner, it does not have a plural form:

* These boxes are for books. The other boxes are for clothes.
Not: The others boxes …

When other as a pronoun refers to more than one person or thing, it takes the plural form, others:

* Some scientists think we should reduce the number of flights to prevent global warming; others
disagree.
Not: … other disagree.

Other must have a determiner before it when it comes in front of a singular countable noun. If the
noun is indefinite (e.g. a book, a woman, an idea), we use another:

* I’ve posted the first package. What shall I do with that other package?
Not: What shall I do with other package?

* After a month in Bolivia, I was ready to move to another country.

 Not: … to move to other country.

We write another as one word: 

* There is another car park a little further down the same street.
Not: There is an other car park …

Another is singular. We don’t use it with plural nouns:

* Other interesting places to visit include the old harbour and the castle.
Not: Another interesting places to visit …