Learn Hardcore German: Es gibt im Garten viele bunte Blumen. - There are many colorful flowers in the garden.

In this sentence, Es gibt im Garten viele bunte Blumen. means There are many colorful flowers in the garden.
You use es gibt to state that something exists or is present.
The thing that exists (viele bunte Blumen) always goes in the accusative case after es gibt.

Why is it gibt (3rd person singular) even though Blumen is plural?

In es gibt, the verb gibt always stays 3rd person singular, no matter whether the following noun is singular or plural.

Grammar-wise, es is a dummy subject (it does not refer to anything).
gibt is just the 3rd person singular of geben used in this fixed construction.
You say:
- Es gibt einen Garten. – There is a garden.
- Es gibt viele Gärten. – There are many gardens.
The verb does not change to match Blumen; it is fixed as es gibt.

Which case is viele bunte Blumen, and why?

Viele bunte Blumen is in the accusative plural.

After es gibt, the following noun phrase is always in the accusative.
Blumen is plural of die Blume, and in the plural the nominative and accusative look the same: die Blumen.
So:
- Singular accusative: Es gibt eine bunte Blume.
- Plural accusative: Es gibt viele bunte Blumen.

Why is it bunte and not something like bunter or bunten?

The adjective bunte (colorful) takes the ending -e here because it comes after the word viele and before a plural noun.

Pattern: viele + adjective + plural noun → the adjective usually ends in -e.
- viele schöne Häuser
- viele alte Bücher
- viele bunte Blumen
Formally: viele already carries a plural ending, so the adjective gets a simple -e in the nominative and accusative plural.

What is the difference between viel and viele? Why is it viele here?

viel is used with uncountable nouns (stuff you do not usually count one by one):
- viel Wasser – much water
- viel Zeit – much time
viele is the plural form used with countable nouns:
- viele Bücher – many books
- viele Häuser – many houses
- viele Blumen – many flowers

Since Blumen are countable, you use viele bunte Blumen, not viel bunte Blumen.

What does im mean, and where does it come from?

Im is a contraction of in dem.

in = in
dem = the (dative masculine or dative neuter singular)
in dem Garten → im Garten

So im Garten literally means in the garden in the dative case.

Why is it im Garten (dative) and not in den Garten (accusative)?

The preposition in can take either dative or accusative, depending on the meaning:

Dative: location (where something is)
- im Garten – in the garden (location)
Accusative: direction / movement (where something is going)
- in den Garten gehen – to go into the garden

In Es gibt im Garten viele bunte Blumen., we are talking about where the flowers are (location), so in takes the dative → im Garten.

Can I change the word order? For example, can I say Im Garten gibt es viele bunte Blumen?

Yes, German word order is flexible, and both sentences are correct:

Es gibt im Garten viele bunte Blumen.
Im Garten gibt es viele bunte Blumen.

The meaning is basically the same (There are many colorful flowers in the garden), but the emphasis changes slightly:

Starting with Es gibt is more neutral, just stating existence.
Starting with Im Garten emphasizes the place first: In the garden, there are many colorful flowers.

You can also put im Garten at the end:
Es gibt viele bunte Blumen im Garten.
That emphasizes viele bunte Blumen more, and the garden is added as extra information.

What is the difference between es gibt im Garten viele bunte Blumen and im Garten sind viele bunte Blumen?

Both are understandable, but there is a nuance:

Es gibt im Garten viele bunte Blumen.
Focus on existence / availability: There are (there exist) many colorful flowers in the garden.
Im Garten sind viele bunte Blumen.
More like In the garden are many colorful flowers. It sounds slightly more descriptive, focusing on where the flowers are.

In practice, both can often translate as There are many colorful flowers in the garden, but es gibt is the standard way to say there is / there are in many contexts.

How do I negate this sentence? How do I say there are no colorful flowers in the garden?

You usually negate es gibt with kein:

Es gibt im Garten keine bunten Blumen.
→ There are no colorful flowers in the garden.

Details:

keine is the accusative plural of kein, matching Blumen.
The adjective changes to bunten because keine behaves like an article:
- keine bunten Blumen

You can also say:

Es gibt im Garten nicht viele bunte Blumen.
→ There are not many colorful flowers in the garden.
Here nicht negates viele, not the existence of flowers altogether.

How do I say this sentence in the past or future with es gibt?

You change the verb form of geben:

Past (simple past / Präteritum):
Es gab im Garten viele bunte Blumen.
→ There were many colorful flowers in the garden.
Present perfect (spoken past):
Es hat im Garten viele bunte Blumen gegeben.
→ There have been / there were many colorful flowers in the garden.
Future:
Es wird im Garten viele bunte Blumen geben.
→ There will be many colorful flowers in the garden.

The structure es + [form of geben] + … stays the same; only the verb form changes.

What is the singular of Blumen, and what article does it take?

The singular is die Blume (feminine).

Singular:
- die Blume – the flower
- eine Blume – a flower
Plural:
- die Blumen – the flowers (no -n on the article in nominative/accusative plural)
- In our sentence we have: viele bunte Blumen (many colorful flowers).

So the full singular version of the sentence would be:
Es gibt im Garten eine bunte Blume. – There is a colorful flower in the garden.