Big Data usually includes data sets whose size exceeds the capabilities of commonly used computer tools to capture, manage, and process data in a reasonable amount of time. Big Data is defined as three-dimensional, with those being volume, velocity, and variety. Relational databases are inadequate for processing such large data sets. Non-relational databases, on the other hand, are more scalable, show better performance and solve many problems that relational databases are not designed to solve. Many techiques, technologies, and tools were developed to manage Big Data, one of them being Apache Hadoop. Apache Hadoop, or just Hadoop, is framework for distributed storage and processing of large data sets on computer clusters composed of one to several thousand computers built from commodity hardware. Hadoop filesystem (HDFS), YARN platform for resource management and MapReduce programming model, which are covered in the paper in detail, form the base of Hadoop. In the fifth chapter, using Hadoop framework and MapReduce programming model on a small computer cluster, MapReduce software is implemented for sorting integer numbers that are read from input file.