Hello, I am Yoshi from NILS Japanese language school. You will learn more in Lesson 14.
[V ます-form しましょうか] Shall I…?
This expression is used when the speaker is offering to do something for the listener.
(Example)
A: 傘（かさ）を　貸（か）しましょうか。　　Shall I lend you an umbrella?
B: すみません。お願（ねが）いします。　　Yes, please.

A: 荷物（にもつ）を　持（も）ちましょうか。　　Shall I carry your parcel?
B: いいえ、けっこうです。　　No, thank you.

[S1が、S2] …, but…
(Example)
失礼（しつれい）ですが、　お名前（なまえ）は？
Excuse me, but may I have your name?
すみませんが、塩（しお）を　取（と）って　ください。
Please pass me the salt.

You learned the conjunctive particle が in Lesson 8. In expressions such as しつれいですが or すみませんが, which are used as introductory remarks when speaking to someone, が, losing its original meaning, is used to connect two sentences lightly.

September 12th News, from NILS Japanese language school.