Much is used with uncountable nouns; its meaning is akin to a lot (of), and lots (of) Many grammar books for learners and English websites advise that much should only be used in questions and in negative sentences, but that's an oversimplification, it can also be used in affirmative sentences.
How much fear and distrust is there in the world? (interrogative)
There is a lot of fear and distrust in the world.
There is much fear and distrust in the world. (formal)
There isn't a lot we can do (pronoun)
There isn't much we can do (pronoun)
There isn't a lot of time left.
There isn't much time left.
A lot of fun was had by all.
Much fun was had by all. (formal)
A lot of money was spent on buying drinks.
Much money was spent on drinks. (formal)
The authoritative Advanced Grammar in Use by Martin Hewings says:

In affirmative sentences we generally use a lot of and lots (of) rather than much (of) and many (of), particularly in informal contexts. However, there are a number of exceptions–
In formal contexts, such as academic writing, much (of) and many (of) are often preferred. […]
- Much debate has been heard about Thornton's new book
- Much of her fiction describes women in unhappy marriages
In formal contexts we can use much and many as pronouns:
- There is no guarantee she will recover. Much depends on how well she responds to treatment.
From Wiktionary we also have the following examples
- They set about the task with much enthusiasm. (also a lot of enthusiasm)
- Add this much water and no more (this much is indicating a specific quantity, without changing the meaning it is not replaceable by “a lot of”.)
- Take as much time as you like. (also: as long as)
- I have much hope for the future. (In this instance, much is modifying the uncountable noun hope)
- I have much need for a new assistant.
- He left her, much to the satisfaction of her other suitor. (In this instance, much to is not replaceable by a lot of)
- From those to whom much has been given, much is expected. (Luke 12:48)
The Biblical quote was the inspiration for John F Kennedy's famous line
For of those to whom much is given, much is required. And when at some future date the high court of history sits in judgment on each one of us–recording whether in our brief span of service we fulfilled our responsibilities to the state–our success or failure, in whatever office we may hold, will be measured by the answers to four questions…
All the affirmative sentences with much are grammatical, and they will sound formal to native speakers. But in everyday speech and informal writing, the expressions a lot (of)–and even more informal–lots (of), will usually be preferred.