A grammar compression algorithm, called GCIS, is introduced in this work. GCIS is based on the induced suffix sorting algorithm SAIS, presented by Nong et al. in 2009. The proposed solution builds on the factorization performed by SAIS during suffix sorting. A context-free grammar is used to replace factors by non-terminals. The algorithm is then recursively applied on the shorter sequence of non-terminals. The resulting grammar is encoded by exploiting some redundancies, such as common prefixes between right-hands of rules, sorted according to SAIS. GCIS excels for its low space and time required for compression while obtaining competitive compression ratios. Our experiments on regular and repetitive, moderate and very large texts, show that GCIS stands as a very convenient choice compared to well-known compressors such as Gzip 7-Zip; and RePair the gold standard in grammar compression; and recent compressors such as SOLCA, LZRR, and LZD. In exchange, GCIS is slow at decompressing. Yet, grammar compressors are more convenient than Lempel-Ziv compressors in that one can access text substrings directly in compressed form without ever decompressing the text. We demonstrate that GCIS is an excellent candidate for this scenario, because it shows to be competitive among its RePair based alternatives. We also show that the relation with SAIS makes GCIS a good intermediate structure to build the suffix array and the LCP array during decompression of the text.