adverb, noun which may take the genitive case particle 'no'
Formal or literary adverb meaning 'in this manner' or 'like this'. Often used in written language or formal speech to refer to something just mentioned.
かくして、長い会議は終わった。
Thus, the long meeting came to an end.
問題はかくのごとく解決された。
The problem was solved in this manner.
こう is the common, everyday word for 'like this' or 'in this way'. かく is more formal and literary, often used in set phrases or written language.
このように is a more explicit and slightly formal phrase meaning 'in this way'. かく is more concise and literary.
From classical Japanese adverb かく, meaning 'in this way'. The kanji 斯 is an ateji (phonetic borrowing) used for its meaning 'this, thus'.