Can you recommend me series to watch?

No detective show, but if you enjoyed Monk you should try "The Marvelous Mrs. Maisel". Tony Shalhoub is simply amazing!

For comedy, i suggest Brooklyn Nine Nine
For crime, i suggest Peaky Blinders

I would recommend these:
Lethal Weapon-https://www.imdb.com/title/tt5164196/
Person of Interest-https://www.imdb.com/title/tt1839578/
True Detective-https://www.imdb.com/title/tt2356777/
Mindhunter-https://www.imdb.com/title/tt5290382/
The Wire-https://www.imdb.com/title/tt0306414/

Peaky Blinders
https://www.netflix.com/title/80002479

It's an old series, but have you ever watched Poirot? :)

For detective/police stuff I can definitely recommend 11.22.63, The Killing (English remake of Forbrydelsen, both are great), The Shield

https://www.csfd.cz/uzivatel/79859-w1ll-1-4m/hodnoceni/?pof2-filter=3 are TV series rated by me, page is in Czech, but if you open something, there's an english name of that show also.

black books :D

Nathan for You and Review both are comedy gold shows. Cobra Kai pretty great comedy as well. From drama i enjoyed The Night Of, Mindhunter, Trust

The terror is a really good new series, the shooter is fine too.

Castle - for detective show
Better off Ted - comedy show

I like detective shows

Check that: https://en.wikipedia.org/wiki/Life_on_Mars_(U.S._TV_series)

Limitless
https://www.imdb.com/title/tt4422836/

Person of Interest! It fits the "cop" shows theme you watch but it has a twist (especially later episodes) I can't recommend it enough.
And for comedy, maybe Brooklyn 99?

If you haven't seen True Detective yet, then it's time now.

The Good Cop, based on an Israeli original, starring Josh Groban(?!) and Tony Danza not sure if he's been in anything since Who's The Boss
The Good Doctor, based on a Korean original, starring Freddie Highmore.
The Rookie has Nathan Fillion, so enough said.

The Crown
Lost In Space

OMG, you actually watched Boku no Piko. I haven't and will never watch it because it's notorious...
...but... WHY? lol.

Most of the good ones have already been mentioned above. (Person of Interest is awesome)

Since you like Detective Series:
The Killing (Netflix series. It's really good)

Oh, since you like animated series too:
99 Days (Gangster series set during prohibition America)

Arrested Development - Comedy
The wandering samurai - Anime
Better call Saul - Drama

Sharp Objects, really good series

lethal weapon (With defectives)
The good doctor (i think a unique series with surgeon/doctor)
The 100 (earth becoming uninhabitable for some years, and some humans return again there with unexpected things)
Forever (TV Series 2014–2015) (a man with an unexpected curse, to Never die! that help a defective with his skill)
Spartacus (With arena fights on the Glory Rome)

I love Designated Survivor. You can see it on Netflix. Altered Carbon is great too, so is Lucifer. Actually all the ones that have been recommended are very good. Check out Netflix, Amazon, and Hulu. You can watch most great series on one of these, usually without commercials.

"Castle" and "Bosch" are cool detective series.

Lucifer - Best detective/comedy serie !

Sharp object

I'm currently watching (and thoroughly enjoying) Travellers on Netflix.
Time travel done differently, and with consistency. Also, being centered on a team that has missions to perform gives it a decent procedural feel.