In the early Cyrillic alphabet there was little or no distinction between the letters и (izhe) and і (i), descended from the Greek letters η (eta) and ι (iota). They both remained in the alphabetical repertoire because they represented different numbers in the Cyrillic numeral system, eight and ten, and are therefore sometimes referred to as octal I and decimal I.
I (decimal I, dotted I) also used to be in the Bulgarian alphabet before 1878 and Russian alphabet before 1918, when a significant reform of the Russian orthography came into effect. For the rules governing the usage of it in the "old" Russian orthography, see Russian alphabet#Letters eliminated in 1918.
(b) write "и" before consonants and as the last letter of a word
(c) exception 1: write "и" before (semi)vowels in compound words (пятиакровый: пяти+акровый, five-acre)
(d) exception 2: write "и" in "миръ" for "peace, tranquility, concord, union", and "i" in "мiръ" for "world, universe, local community, commons, society, laity", with all derived words.