Indeclinable nouns are those nouns which have the same form in all cases.
Мужчина в пальто - A man in coat.
Без пальто очень холодно - It is cold without a coat.
Нужно пришить пуговицу к пальто - One needs to sew the button on a coat.
Among such nouns there are as common nouns (cacao, cinema, cafe), as proper nouns, such as names of cities (Sochi, Oslo) or names and surnames (Camus).
Indeclinable nouns are usually the words of foreign origin, which end with the vowels Е, И, О, У, Ю.
Радио - radio, метро - metro, табло - indicator board.
They can also be surnames of the feminine gender ending with a consonant, -О, -ИХ, -ЫХ.
Войнич - Voynich, Коваленко - Kovalenko, Седых - Sedykh.
We also refer to indeclinable nouns shortenings and abbreviations.
ЮНЕСКО - The UNESCO, США - The USA.
It might seem that indeclinable nouns are much easier than declinable ones because you should not think about cases and changes in endings, but in fact it's not true. On the contrary, when we deal with such words in a sentence, we should agree them with other words, so there is the question - for example, adjective of what gender should we use?
There are their own declension rules for different categories of indeclinable nouns.
Geographical names are declined according to the gender of a common name which they denote.
Сочи (Sochi) - a city, that is why Сочи - masculine gender.
Abbreviations are declined according to a main word.
ООН (UN) - Организация Объединённых Наций (the United Nations organization), that is why ООН - feminine gender.
Indeclinable nouns of foreign origin are often declined as neuter gender.
Такси - taxi, радио - radio, какао - cacao.
Exceptions: кофе - coffee (masculine gender), авеню - avenue (feminine) and some more words.
If a foreign word obviously belongs to the feminine gender, e.g. describes a woman, then it is declined as feminine gender.
Элегантная мадам (feminine gender) - An elegant madam.