Historia tego miasta jest ciekawa.

Because historia in this sentence means the history of ..., and in Polish that of relationship is usually shown with the genitive case.

So:

• miasto = city (basic dictionary form, nominative)
• miasta = of the city (genitive singular)

And the demonstrative must match it:

• to miasto = this city
• tego miasta = of this city

So Historia tego miasta literally means History of this city.

Miasta is genitive singular of miasto.

The noun miasto is neuter, and its forms include:

• miasto — nominative singular
• miasta — genitive singular

In this sentence, miasta is in the genitive because it depends on historia:

• historia miasta = the history of the city
• historia tego miasta = the history of this city

Tego is the genitive singular form of ten / to / ta (this).

It agrees with miasta, not with historia.

Since:

• miasto is neuter
• miasta is genitive singular

the matching form of this is tego.

So:

• to miasto = this city
• tego miasta = of this city

A helpful way to think about it is that tego miasta works as one unit: of this city.

Because it agrees with historia, which is a feminine noun.

In Polish, adjectives must agree with the noun they describe in gender, number, and case.

Here:

• historia = feminine singular
• ciekawa = feminine singular form of interesting

Compare:

• ciekawy — masculine
• ciekawe — neuter
• ciekawa — feminine

Since historia is feminine, the sentence needs ciekawa.

Jest means is. It is the 3rd person singular present form of być (to be).

So the sentence structure is:

• Historia tego miasta — subject
• jest — is
• ciekawa — predicate adjective (interesting)

Literally: The history of this city is interesting.

In a normal, standard sentence like this, no—you should keep jest.

Polish sometimes allows omission of to be in certain styles, headlines, notes, or very informal speech, but:

• Historia tego miasta jest ciekawa. — standard, natural
• Historia tego miasta ciekawa. — sounds incomplete, marked, or non-standard in ordinary use

So for learners, the safe rule is: keep jest here.

Not completely. Polish word order is more flexible than English, because case endings show grammatical relationships.

The neutral version is:

• Historia tego miasta jest ciekawa.

But other orders are possible for emphasis, for example:

• Ciekawa jest historia tego miasta.
  = Interesting is the history of this city / The history of this city is interesting
  This emphasizes ciekawa.

Still, the original order is the most straightforward and natural for a learner.

Because Polish does not have articles like a/an and the.

So:

• historia can mean history, a history, or the history
• miasto can mean city, a city, or the city

Context tells you which meaning is intended.

In Historia tego miasta jest ciekawa, English needs the:

• The history of this city is interesting

But Polish expresses that without any article.

It can mean both, depending on context.

Common meanings include:

• history — as in the past of something
• story — as in an account or narrative

In this sentence, because we have tego miasta (of this city), the natural meaning is:

• the history of this city

If you were talking about a tale or anecdote, context would usually make that clear.

A simple pronunciation guide is:

hee-STO-rya TE-go MYA-sta yest chye-KA-va

A few notes:

• historia → stress on sto: hi-STO-ria
• tego → TE-go
• miasta → MIA-sta
• jest → sounds roughly like yest
• ciekawa → chie-KA-va or chye-KA-va

Polish stress is usually on the second-to-last syllable, and that works for all the words in this sentence.

Yes. That means The history of the city is interesting or A city's history is interesting, depending on context.

The difference is:

• Historia miasta jest ciekawa. — The history of the city / the city's history
• Historia tego miasta jest ciekawa. — The history of this city

So tego adds the idea of this specific city.

You change jest and keep the rest the same.

• Historia tego miasta była ciekawa.
  = The history of this city was interesting.

• Historia tego miasta będzie ciekawa.
  = The history of this city will be interesting.

Also notice that ciekawa stays feminine because it still agrees with historia.

Yes, very often it works that way.

• Historia tego miasta = the history of this city
• very naturally in English: this city's history

Polish usually prefers this noun + genitive structure instead of using something exactly like English 's.

So a good learner shortcut is:

• X Y-genitive often means Y's X or the X of Y.