A gene library is a large collection of DNA fragments cloned from an organism. It contains genomic DNA or cDNA sequences. Gene libraries are constructed using molecular tools like restriction enzymes and ligases to cut and paste DNA fragments into vectors such as plasmids, phages, or artificial chromosomes. The choice of vector depends on the size of the genome being cloned. Libraries allow screening to identify genes of interest through techniques like hybridization or expression screening. cDNA libraries contain only expressed sequences without introns, making them preferable for cloning eukaryotic genes in prokaryotes.