"Chinese" / "중국어"

Once again, strolling the streets as is my fashion, I've noticed the plethora of signs for language institutes claiming to teach "Chinese". Is it only me that finds this remarkably odd? I've not once seen signs for "Mandarin" or "Cantonese" or in fact any other dialect spoken in that vast and populous country up north. Only "Chinese".

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From ChinaLanguage.com
Chinese has seven major language groups of which the Mandarin language group forms the largest group. The Mandarin group consists of a wide range of dialects in the northern, central, and western regions. The Cantonese dialects are spoken in Hong Kong, Guangdong, Southern Guangxi Zhuang Autonomous Region, parts of Hainan, Macau, and in many overseas settlements. The Hakka (Kejia) languages are spoken in Guangdong, southwestern Fujian, Jiangxi, Hunan, Yunnan, Guangxi, Guizhou, Sichuan, Hainan, Taiwan, Singapore, Malaysia, Indonesia, many overseas Chinese communities, and in pockets throughout Southeast Asia.

(And that's not to mention the Xiang dialects, the Min dialects, the Gan dialects, and the Wu dialects.)

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From an English-Korean dictionary:
Mandarin 베이징 관화(官話) [The standard language of Beijing]
Cantonese 광둥(廣東)어 ['Guangdong lanugage']
Hakka 하카어 ['Hakka language']

See, Korean does have words for all of them!

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Or from Wikipedia:
The Chinese language (汉语/漢語, 华语/華語, or 中文) is a tonal language and a member of the Sino-Tibetan family of languages. Although Chinese is often regarded for cultural reasons as a single language, its range of regional variation is comparable to or greater than that of the Romance languages.
China ... maintained a common written language throughout its entire history, despite the fact that its actual diversity in spoken language has always been comparable to Europe.

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From a Korean dictionary:
中國語 <명사> 중국 사람들이 쓰는 언어. 중국 본토와 주변 지역을 중심으로 한민족(漢民族)이 써 오는 고유한 언어로, 고립어에 속한다.
Chinese noun. The language used by Chinese people. Pertaining to the isolating language particular to the Han peoples of mainland China and surrounding areas.

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I can only assume they mean Mandarin.
In that case, where can folks go to learn Cantonese round here?