普通话 is Mandarin Chinese, a dialect of Chinese, as oppose to Cantonese, etc. 中文 and 汉语 both mean Chinese as a whole (no specific dialect), but 中文 is more about written Chinese and 汉语 is more about spoken Chinese.

just adding some information, 普通 means "common" so that's the name of the Common language in China, because in China there are many languages and everybody must know a common one. 汉 is the last name of a emperor and a dynasty, and in that territory people speak mandarin so mandarin took the name 汉语. 中文 is because... language of 中国 is just 中文 like the language of 英国 is 英文.

普通话 = 汉语 = oral Chinese language 中文 = written Chinese language

Putonghua (普通话) is Mandarin, our government language and on TV. Zhongwen (中文Chinese language) can be Mandarin, but broad meaning, it means all languages in China, could be Shanghainese, Cantonese, Tibet. Hanyu (汉语) means the Han nationality's language, which is mandarin come from. So you are learning Hanyu, our Han people's language, not Man people, Miao people, or other 55 minorities language. Regards.

in fact.there are no differend.中文=汉语>普通话。,