Pazartesi akşamı parkta yürümek istiyorum.

Breakdown:

• Pazartesi – Monday
• akşam-ı – evening-its → Monday evening (literally: the evening of Monday)
• park-ta – park-in/at (locative case)
• yürü-mek – to-walk (infinitive)
• ist-iyor-um – want-(present continuous)-I

So overall: I want to walk in the park on Monday evening.

Pazartesi akşamı is a common noun compound in Turkish, literally Monday’s evening:

• akşam = evening
• akşam-ı = its evening (3rd person possessive suffix)

In compounds like Pazartesi akşamı, Turkish uses this -ı / -i / -u / -ü ending on the second noun:

• Pazartesi akşamı – Monday evening
• Salı sabahı – Tuesday morning
• Cuma gecesi – Friday night

The possessive idea is not strongly felt in meaning; it’s just how Turkish forms many time expressions. Saying Pazartesi akşam would be incorrect.

This is how indefinite noun compounds work in Turkish:

• First noun: no ending (Pazartesi)
• Second noun: takes -(s)I possessive (akşam-ı)

So Pazartesi akşamı literally behaves like X’s Y:

• Pazartesi akşamı – Monday’s evening
• kitap kapağı – the book’s cover
• okul bahçesi – the school’s yard

In these compounds, the first part (Pazartesi) is left bare, and the second part (akşamı) carries the marker.

-ta / -te / -da / -de is the locative case in Turkish, meaning in, at, on.

• park – park
• park-ta – in the park / at the park

You use the locative case for locations:

• evde – at home / in the house
• okulda – at school
• parkta – in the park

So parkta yürümek = to walk in the park.

After istemek (to want), Turkish usually uses the infinitive form of the verb (-mek / -mak):

• yürümek istiyorum – I want to walk
• gitmek istiyorum – I want to go
• yemek istiyorum – I want to eat

English also uses the infinitive after want: I want to walk, not I want I am walking.

So yürümek istiyorum is exactly parallel to I want to walk.
Yürüyorum would be a separate verb (I am walking), not something you attach directly after istiyorum.

You can say yürümeyi istiyorum, but it sounds more formal/marked and is less common in everyday speech.

• yürümek istiyorum – normal, very common
• yürümeyi istiyorum – technically correct, but feels heavier or more emphatic, like “I desire the act of walking”

Grammatically:

• yürü-mek – infinitive
• yürü-me-yi – verbal noun + accusative (literally “the act of walking” as a direct object)

With istemek, the plain infinitive (yürümek) is what you will hear most in normal conversation.

In yürümek istiyorum, istiyorum already carries:

• the tense/aspect (present continuous: -iyor)
• the person (1st person singular: -um)

The subject “I” applies to the whole verb group yürümek istiyorum. You don’t repeat the person ending on the infinitive:

• yemek istiyorum – I want to eat
• gitmek istiyoruz – we want to go
• konuşmak istiyordun – you wanted to speak

The person ending always goes on the finite verb (istiyorum), not on the infinitive.

Turkish word order is flexible, but verb-final is the norm. Variants include:

• Pazartesi akşamı parkta yürümek istiyorum. (neutral, very natural)
• Parkta Pazartesi akşamı yürümek istiyorum. (slight emphasis on park)
• Pazartesi akşamı yürümek istiyorum parkta. (unusual in speech; sounds stylized or poetic)

The most natural everyday choice is the original: time (Pazartesi akşamı), place (parkta), then the verb phrase (yürümek istiyorum), with the conjugated verb last.

Yes, you can, but the meaning changes slightly:

• Pazartesi parkta yürümek istiyorum. – I want to walk in the park on Monday (no time of day specified)
• Pazartesi akşamı parkta yürümek istiyorum. – I want to walk in the park on Monday evening (specifically in the evening)

So omitting akşamı makes the sentence more general about Monday as a day.

In standard Turkish spelling, days of the week and months are capitalized:

• Pazartesi, Salı, Çarşamba, Perşembe, Cuma, Cumartesi, Pazar
• Ocak, Şubat, Mart, …

So Pazartesi akşamı parkta yürümek istiyorum correctly capitalizes Pazartesi.