This review discusses the application of atom interferometry in modern science, focusing on its role in fundamental quantum science, precision metrology, and atomic and molecular physics. The article outlines the basic tools for coherent atom optics, including diffraction by nanostructures and laser light, three-grating interferometers, and double wells on atom chips. It reviews scientific advances in various fields that have resulted from the application of atom interferometers, grouped into three categories: (i) fundamental quantum science, (ii) precision metrology, and (iii) atomic and molecular physics. The focus is on linear matter wave optics, where each single atom interferes with itself. The article also discusses the historical development of atom interferometry, its applications in precision measurements such as gravimeters, gyroscopes, and gradiometers, and its use in studying fundamental phenomena like decoherence, phase shifts, and the behavior of Bose-Einstein condensates. The review highlights the advantages of atom interferometry, including its ability to measure very small potential energies with high precision, and its potential for future applications in atomic physics and quantum technology.This review discusses the application of atom interferometry in modern science, focusing on its role in fundamental quantum science, precision metrology, and atomic and molecular physics. The article outlines the basic tools for coherent atom optics, including diffraction by nanostructures and laser light, three-grating interferometers, and double wells on atom chips. It reviews scientific advances in various fields that have resulted from the application of atom interferometers, grouped into three categories: (i) fundamental quantum science, (ii) precision metrology, and (iii) atomic and molecular physics. The focus is on linear matter wave optics, where each single atom interferes with itself. The article also discusses the historical development of atom interferometry, its applications in precision measurements such as gravimeters, gyroscopes, and gradiometers, and its use in studying fundamental phenomena like decoherence, phase shifts, and the behavior of Bose-Einstein condensates. The review highlights the advantages of atom interferometry, including its ability to measure very small potential energies with high precision, and its potential for future applications in atomic physics and quantum technology.