In this book the new notion of interval semirings are introduced. New structures like interval groups are used to construct interval group semirings. Further non-associative interval semirings are constructed using loops and groupoids. We have given 284 examples, 118 problems are proposed ¿ some of them at the research level.The main keywords are interval semirings, interval groups, interval matrix semirings, interval groupoid semirings, neutrosophic interval semirings, and loop interval semirings.