By grouping the う-Verb 従（したが）う ‘to comply’ with に, a common pattern meaning ‘to comply with (A)’, ‘in accordance with (A)’, or ‘following (A)’ will be created. This is a fairly strong and formal structure, indicating that (B) is being controlled or heavily influenced by (A). (B) will often express some kind of ongoing or sudden change caused by (A).
に従（したが）って may appear after either verbs of nouns in their dictionary forms.

• 年（とし）を取（と）るに従（したが）って、目（め）がどんどん悪（わる）くなっていってる気（き）がする。
  I feel like my eyes are getting worse and worse as I get older.
• テレワークの普及（ふきゅう）が進（すす）むに従（したが）って、通勤（つうきん）するサラリーマンが減（へ）っていっている。
  As teleworking becomes more widespread, the number of office workers commuting to work is decreasing.
• 僕（ぼく）はただ上司（じょうし）の指示（しじ）に従（したが）って仕事（しごと）を進（すす）めていただけです。
  I was just following my boss's instructions to get the job done.
• この説明書（せつめいしょ）に従（したが）って、パソコンの初期（しょき）設定（せってい）を行（おこな）ってください。
  Please follow these instructions to perform the initial setup of your computer.

As this expression is quite formal, it is common to see it used in relation to matters that are usually discussed in formal or official situations, such as laws, standards, conventions, or traditions.