Learn Russian: У моего дедушки много лошадей.

The word много (many) requires the noun that follows it to be in the genitive plural case. The dictionary form of "horse" is лошадь, which is a feminine noun ending in a soft sign (-ь). To make nouns ending in -ь genitive plural, we drop the soft sign and add -ей, giving us лошадей.

Normally we use есть to say someone has something. Why is it missing in this sentence?

You are right that "My grandfather has a horse" would normally be У моего дедушки есть лошадь. However, when we specify a quantity like много (many), мало (few), or a number, we drop есть. The focus of the sentence shifts from whether he has horses to how many he has.

Why do моего and дедушки have different types of endings?

The phrase "my grandfather" must be in the genitive case because it follows the preposition у. Дедушка is a masculine person, but because the word ends in -а, it takes feminine-style endings when it changes form (so -а becomes -и). However, adjectives and pronouns like мой strictly follow the noun's actual gender (masculine). So, мой changes to the standard masculine genitive form, моего.

How do I pronounce the word ?