Kanji writing originated from Chinese, but the hiragana and katakana writing systems originated in Japan, based on the Chinese characters (see How did katakana and hiragana originate?).
Japanese is unusual in having a writing system that is "syllabic". Each hiragana (平仮名) or katakana (片仮名) except one corresponds to either a vowel or a combination of a consonant plus a vowel. (The exception is the syllabic n, written ん or ン. See What is syllabic n?) Precisely, each of the kana corresponds to one mora (see What is the difference between a mora and a syllable?).
The kana have more than one possible ordering. These are discussed in What is the origin of the gojūon kana ordering? and How does the i-ro-ha ordering go? For methods of remembering the kana ordering, see Is there a mnemonic for remembering the order of kana signs? Some history of the kana and the reason for the gaps in the kana chart in the "y" column appear in Is there a kana symbol for ye or yi?
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