Ｘによると ("according to X") was introduced in Lesson 23 as part of the hearsay pattern. Be sure to distinguish it from Ｘによって explained below.

Ｘによって means "depending on X." Be sure to distinguish it from Ｘによると explained above.

	Ａ： ジョージアの冬は暖かいですか。 Ｂ： 年によってちがいますね。	A: Is Georgia's winter warm? B: It depends on the year. (Lit. "It differs depending on the year.")
	国(くに)によってことばがちがいます。	Depending on the country, languages are different.
	アパートによって、やちんは高かったり、 安かったりします。	Depending on the apartments, the rent is sometimes expensive or sometimes cheap.

The combination of Verb-stem + 直す creates a compound verb that means "to V again" or "to re-V" in order to correct it. (The kanji 「直」 means "straight" or "correct.")

Don't confuse this with V-stem + かえる. For example, 書き直す means "to write again (to correct some problems)" while 書きかえる means "to revise/rewrite it (not necessarily to correct any problems)."

V1 (stem)	V2
かき (write) よみ (read) み (look) おもい (think) いい (say) えらび (select) やり (do) しらべ (check)	なおす (fix)	to rewrite/correct to reread/read again to review/look again to rethink/think again to say it again correctly to reselect to redo to recheck

	もう一度読み直したら、よくわかりました。	When I reread it, I understood it well.
	テストを出す前に、見直したほうがいいですよ。	Before you submit the quiz, you'd better review it.
	まちがっているから、やり直して下さい。	Because it's wrong, please do it again.

The combination of Vて + くる was introduced in Lesson 18 as an errand pattern "come back having V-ed" or "go and V." The combination Vて + くる can also express the notion that "something begins to V." However, unlike Ｖ-stem + だす or V-stem + はじめる. the Vて + くる can only refer to phenomena that happen without someone's deliberate intervention such as changes in weather or other "uncontrollable"or "natural" events. These pheonomena or events are often experienced as something that approaches from outside toward the speaker.

Vて	くる
ふって (rain/snow) ふいて (blow) わかって (understand) 暖かく なって (become warm) 春に なって (become spring)	くる (come)	begin to rain/snow [wind] begins to blow begin to understand begin to warm up begin to become spring

Note that the particle に is required after a noun or な-adjective (e.g., べんりになってきた) below.

	おゆがわいてきました。	The water began to boil.
	寒くなってきたね。	It started to get cold.
	コーヒーを飲んだのに、ねむくなってきた。	I had a coffee, but I began to feel sleepy.
	コンピュータはべんりになってきた。	Computers have become more convenient.

The expressions above can be rephrased as わきはじめる／わきだす ("begin to boil"), 寒くなりはじめる／寒くなりだす ("begin to get cold"), or ねむくなりはじめる／ねむくなりだす ("begin to feel sleepy"), respectively.