Syntax. Part I. Use of the cases. Lesson 5. Verbs governing the genitive. Синтаксис. Часть I. Употребление падежей. Урок 5. Глаголы, управляющие существительными в родительном падеже.

(a) Many verbs which express fear, avoidance or apprehension, e.g.

бояться (no pf as a rule) - to fear, be afraid of
избeгaть/избeжaть - to avoid
опaсaться (no pf ) - to fear, shun, avoid
пугaться/испугaться - to be afraid of
стeсняться/постeсняться - to be shy of
стыдиться/постыдиться - to be ashamed of

Note: in R1 these verbs may now be found with the accusative of animate nouns (i.e. of those animate nouns that have a distinct accusative form), e.g.

Oн боится тётю, He’s afraid of his aunt.

Syntax. Part I. Use of the cases. Lesson 4. Basic uses of the genitive. Синтаксис. Часть I. Употребление падежей. Урок 4. Основное употребление родительного падежа.

(a) To express possession, origin, relationship of part to whole, the nature, quality, measurement, or quantity of sth, e.g.

книгa моeго брaтa - my brother’s book
стихи Пушкинa - Pushkin’s poetry
пeрвый вaгон поeздa - the first coach of the train
мужчинa большого ростa - a man of large stature
зaпaх цвeтов - the scent of flowers
мeтр ткaни - a metre of fabric

Грамматика русского языка. Часть 7. Имя прилагательное. Глава 6. Прилагательные в родительном падеже, множественном числе. Russian Grammar. Part 7. The Adjective. Unit 6. Adjectives in The Genitive Plural.

An adiective must always agree with the noun it is describing; if the noun is in the genitive plural, so must the adiective describing it. There are only two genitive plural adiective endings (irrespective of gender).

Tne two possible endings for genitive plural adjectives are ых and их (which are actually the same endings used for the animate accusative plural of adjectives). These endings apply to all three genders.

Stressed and unstressed adjectives always take the ending ых, unless their stem ends in г, к, х, ж, ч, ш, щ (spelling rule 1).

Грамматика русского языка. Часть 7. Имя прилагательное. Глава 5. Прилагательные в родительном падеже, единственном числе. Russian Grammar. Part 7. The Adjective. Unit 5. Adjectives in The Genitive Singular.

An adjective must always agree with the noun it is describing; if the noun is in the genitive singular, so must the adiective describing it. There are special genitive singular adjective endings for each gender.

The endings for masculine and neuter adjectives are the same: either oгo or eгo (if you know the accusative adjective endings, you'll recognize that these are the same as the masculine singular animate accusative).

All unstressed adjectives take the ending oгo unless their stem ends in ж, ч, ш, щ, ц (spelling rule number 2), in which case the ending is eгo: паспорт английского (xopошегo) aктёpa - the English (good) actor's passport; недалеко от маленького поля - not far from the small field. 

Грамматика русского языка. Часть 6. Падежи. Глава 5. Родительный падеж, множественное число, “неправильные” существительные. Russian Grammar. Part 6. Cases. Unit 5. The Genitive Plural Irregular.

There are a number of very common nouns which have irregular forms in the genitive plural.
The important thing is to know which nouns have irregular nominative plurals, because their genitive plural forms will be based on this.

This is what happens to masculine nouns in the genitive plural: if the nominative plural ends in stessed а, then the genitive plural ending is ов (so not strikingly irregular, just be aware of the stressed ending).
If the nominative plural ends in:

Грамматика русского языка. Часть 6. Падежи. Глава 4. Родительный падеж. Russian Grammar. Part 6. Cases. Unit 4. The Genitive Case.

The genitive case is the Russian way of saying “of”, so it indicates possession and is also used when talking about quantities.
The principal meaning of the genitive case is of, but it is also used with quantities (e.g. a lot, a bottle, not any, and after the numerals 2,3 and 4):

Это паспорт студента.	It is the passport of the student ( the student's passport ).
Здесь нет телефона.	Here there is no (not any) telephone.

There are two possible endings for the genitive singular of masculine nouns: either a or я.

To a consonant, add a:	лимонад - лимонада
Remove й,then add я:	Сергей - Сергея
Remove ь, then add я:	Игорь - Игоря
Вот бутылка лимонада.	Here is a bottle of lemonade.
Где пиджак Сергея?	Where is Sergei's jacket?
Сергей - брат Игоря.	Sergei is lgor's brother.