Sharia Law
 

What is the Sunni view on Sharia Law?

The Shariah is the Sunni view..

The real question is what misunderstandings do Non Muslims have about the Shariah Law.

wikipedia says:
Sunni
Main article: Sunni
In addition to the "Basic Code" of the Qur'an and Sunnah, traditional Sunni Muslims also add the consensus (ijma) of Muhammad's companions (sahaba) and Islamic jurists (ulema) on certain issues. In situations where no concrete rule exists in the sources, law scholars use qiyas — various forms of reasoning, including analogy, to derive law from the essence of divine principles and preceding rulings. The consensus of the community, public interest, and other sources are used as an adjunct to Sharia where the primary and secondary sources allow.[30] This description can be applied to the major schools of Sunni fiqh, which include the Hanafi, Shafi'i, Maliki and Hanbali.


is this correct?

Yes

my meaning is that who has authority over the Sharia law? Caliphates? Ulema?

Authority is meant in what sense?

If it is in the sense of carrying out sentences, that is the duty of the Caliph or his deputy.
If it is in the sense of interpretation of the sources to deduce rulings, that is the duty of the Ulema.
If it is in the sense of passing judgment, that is the duty of the Qadhi.

Just say 'Sharia,' Sharia law is like saying Law Law.

السلام عليكم

It is correct but I will give you this advice since you seem to be new in Islam or interested in Islam, DO NOT TAKE THE RELIGION FROM WIKIPEDIA, it's written by anonymous people with absolutely no qualifications and half of it is incorrect, inaccurate or just straight out lies.

Use the websites of the Islamic scholars and schools if you don't have access to books but NEVER use wikipedia.

The brothers can recommend books for you.