It's all very well pointing people to TV shows but unless they are at an advanced level or subtitles are provided, they will understand very little and soon give up.  That's my experience anyway.

I'm currently using this site, which provides downloadable mp3 recordings and transcripts of dialogues.

https://gloss.dliflc.edu/

Choose Arabic - Levantine

You will find a mixture of material from Lebanon, Syria, Jordan and Palestine dialects.

The site is aimed at English speakers though.

i am syrian!

if anyone wants to learn the syrian dialect just tell me .....

I think TV and web pages can be very helpful to pick up the accent. 

If I'm to recommend one TV show, it would be (بقعة الضوء) (Spotlight), it's a comedy series, made of dozens of sketches, some touch the reality and some are fantasy. Here is a link to the first season https://www.youtube.com/playlist?list=PLOpvfjrLz9uelWroM2CUuzBHOi4WJTZBN. ;

You can also find other shows on the same channel, about drama, tragedy, history and comedy. But be aware that in history shows they speak Standard Arabic. 

And also here is a couple of well known comdey plays

https://www.youtube.com/watch?v=ExBKUysSJaw  "كاسك يا وطن"   "Cheers to my country" 

https://www.youtube.com/watch?v=OdLv0FeZD7g    "غربة"   "Alienation"

https://www.youtube.com/watch?v=F56ldaDrVe0 "ضيعة تشرين" "The village of Tshreen" 

Sorry if some are low quality, but they are very old. 

I agree with the above comments, this question is sensitive. 

Accents differ even from city to city in Syria but the base is the same. I'm not aware of good books for learning it  but I believe that watching Syrian TV shows/series might be helpful if you want to develop your listening skills + you will get to hear a big amount of phrases used in Syria so you could add them to your vocubulary.