This is the basis document for the ATLAS Receiver Algorithms. ATLAS is the single instrument on the ICESat-2 mission. The Receiver (Rx) Algorithms select the signal location in real-time and instruct the hardware to telemeter a vertical band of received time-tags about this signal location. The algorithms are implemented in the Flight Software (FSW) and in the hardware of the Photon Counting Electronics (PCE) cards. The sole purpose of the algorithms is to reduce the telemetry data volume to fit within the downlink constraint while maximizing the probability of downlinking surface signal. All versions of the Receiver Algorithms from version 2.8 onward incorporate our best knowledge of the ATLAS hardware at this time. It presents algorithms that, based on current Simulator testing, satisfy all of the requirements for the Rx Algorithms. Testing during ATLAS Instrument Integration and Testing with the hardware and software implementation of the Rx Algorithms revealed characteristics and responses that required changes to the Rx Algorithms and this document, which are captured in the change record below.All relevant documentation for the Receiver Algorithms can be found on the ICESat-2 Technical Data Management System (TDMS) under the ATLAS Algorithms subsystem.The launch version of the FSW (version 3.1.0) is based upon version 3.7c of this document.