Notwithstanding this zealous kind of complaint, it would appear to me that they had great fun during the third day when after the English lesson they went to the swimming pool.

notwithstanding 是一个复合介词，由 not + with + stand + ing 构成，字面意思是"不站在...对立面"，引申为"尽管、虽然"。这个词比较正式，常用于书面语中表示让步关系。