The observational parameter space that allows us to detect and describe nonsingle stars is enormous. It comes from the fact that binary stars are very numerous, present themselves with a huge variety of physical properties and have signatures in all astronomical fundamental techniques (astrometry, photometry, spectroscopy). It is, therefore, not a surprise that any significant improvement in observational astronomical facilities has an important impact on our knowledge of binaries. We are currently in an era where the development of various large-scale surveys is impressive. Among them, Gaia and LSST are exceptional surveys that have and likely will have a profound and long-lasting impact on the astronomical landscape. This chapter reviews the status of these two projects, and considers how they improve our knowledge of binary stars.

The chapter presents a summary of the present-day understanding of Type Ia supernova progenitors, mostly discussing the observational approach. This chapter is to provide the nonspecialist with a sufficiently comprehensive view of where we stand.

The statistical distributions of main-sequence multiple-star properties reveal invaluable insights into the processes of binary star formation, and they provide initial conditions for population synthesis studies of binary star evolution. Binary stars are discovered and characterised through a variety of techniques. Correcting for their respective selection effects and combining the bias-corrected results is not a trivial process. This is partially because the intrinsic distributions of companion frequency, primary mass M1, orbital period P, mass ratio q and eccentricity e are all interrelated , i.e., f(M1,P,q,e)/= f(M1)f(P)f(q)f(e). In particular, the binary fraction increases with primary mass, especially across short orbital periods, and binaries become weighted towards larger eccentricities and more extreme mass ratios with increasing separation, especially for more massive primaries. Moreover, binary star statistics vary with age, environment and metallicity. This chapter summarises the strengths and limitations of the various observational techniques, and reviews the statistical correlations in the intrinsic (bias-corrected) multiple-star properties.

With the discovery of both binary black hole mergers and a binary neutron star merger, the field of gravitational wave astrophysics has really begun. The LIGO and Virgo detectors will soon improve their sensitivity allowing for the detection of thousands new sources. All these measurements will provide new answers to open questions in binary evolution related to mass transfer, out-of-equilibrium stars and the role of metallicity. The data will give new constraints on uncertainties in the evolution of (massive) stars, such as stellar winds, the role of rotation and the final collapse to a neutron star or black hole. In the long run, the thousands of detections by the Einstein Telescope will enable us to probe their population in great detail over the history of the Universe. For neutron stars, the first question is whether the first detection GW170817 is a typical source or not. In any case, it has spectacularly shown the promise of complementary electromagnetic follow-up. For white dwarfs, we have to wait for LISA (around 2034), but new detections by, e.g., Gaia and LSST will prepare for the astrophysical exploitation of the LISA measurements.

This chapter discusses the population and spectral synthesis of stellar populations. It describes the method required to achieve such synthesis and discusses examples where inclusion of interacting binaries are vital to reproducing the properties of observed stellar systems. These examples include the Hertzsprung–Russel diagram, massive star number counts, core-collapse supernovae and the ionising radiation from stellar populations that power both nearby HII regions and the epoch of reionization. It finally offers some speculations on the future paths of research in spectral synthesis.

With stellar masses in the range of eight to several hundreds of solar masses, massive stars are among the most important cosmic engines. Each individual object strongly impact its local environment, and entire populations of massive stars have been driving the evolution of galaxies throughout the history of the Universe. Over the last two decades, it has become increasingly clear that massive stars do not form nor live in isolation but rather as part of a binary or higher-order multiple system. Understanding the life cycle of massive multiple systems, from their birth to their death as supernovae and long-duration gamma ray bursts, is thus one of the most pressing scientific endeavours in modern astrophysics. In this quest, observations offer a critical insight that both guide theoretical developments and challenge the model predications. This chapter provides an overview of the observational constraints of the multiplicity properties of OB stars obtained since 2010.

Binaries are the most important energy reservoir of star clusters. Via three-body encounters, binaries can reverse the core collapse and prevent a star cluster from reaching equiparition. Moreover, binaries are essential for the formation of stellar exotica, such as blue straggler stars, intermediate-mass black holes and massive black hole binaries.

Color-magnitude diagrams of open clusters reveal many stars that do not fall on cluster main sequences or red giant branches including blue straggler stars, yellow giants, and sub-subgiants. In fact, as many as a quarter of the evolved stars in older open clusters do not fall on standard single-star isochrones. Rather than being anomalies, these stars are following frequently travelled alternative paths of stellar evolution. Most of these stars are in binary systems, and their origins likely stem from mass transfer, mergers and collisions within binaries. This chapter presents an overview of recent observational and modelling work to understand the processes that shape these alternative stellar evolution pathways, including an HST study of the blue straggler population of NGC 188, an abundance study of the blue stragglers of NGC 6819, establishing yellow giants as evolved blue straggler stars using asteroseismology, exploration of a new class of stars known as sub-subgiants, rotational identification of main sequence blue stragglers with Kepler/K2 and new insights into the angular momentum evolution of blue stragglers.

Many aspects of the evolution of stars, and in particular the evolution of binary stars, are beyond our ability to model them in detail. Instead, we rely on observations to guide our often phenomenological models and pin down uncertain model parameters. To do this statistically requires population synthesis. Populations of stars modelled on computers are compared to populations of stars observed with our best telescopes. The closest match between observations and models provides insight into unknown model parameters and hence the underlying astrophysics. This chapter reviews the impact that modern big-data surveys will have on population synthesis, the large parameter space problem that is rife for the application of modern data science algorithms and some examples of how population synthesis is relevant to modern astrophysics.

Like the Sun, the Moon moves eastward relative to the stars but at a faster rate, completing its motion in one month. The apparent motion of the Moon relative to the Sun produces the cycle of lunar phases as well as both lunar and solar eclipses. Ancient Greek mathematicians devised ways of estimating the distances and sizes of the Sun and Moon from observational data, including the phenomenon of parallax. The planets, too, appear to move relative to the stars. They generally move eastward relative to the stars but occasionally they halt their eastward motion and move westward (in retrograde motion) before resuming their normal eastward trek. The planets can be classified into two groups, inferior and superior, each of which displays certain characteristics of motion.

The ancient Greek mathematician Eudoxus developed a model for the motion of the Sun, Moon, and planets in which each body was carried around on a series of nested spheres that were all centered on Earth. Eudoxus’ geocentric model was incorporated into the highly successful cosmology of Aristotle. However, this model was unable to account accurately for the observed motions of the planets. Later astronomers such as Hipparchus and Ptolemy developed a new set of models in which each planet is carried around a circular epicycle, which in turn is carried around a circular deferent with its center near the Earth. Ptolemy even used these models to estimate distances to each planet. Although these models were quite accurate, they did suffer from some problems and were criticized or modified by medieval scholars.

This appendix provides mathematical details to supplement the ideas presented in the main text. Topic covered include: angular measurement, apparent diameter, trigonometry, finding the Sun’s altitude from the length of a shadow, determining the relative distances of the Sun and Moon, and finding the distance to an astronomical object using parallax measurements. In addition, this appendix shows how to calculate the sizes of epicycles in the Ptolemaic theory and the periods and sizes of planetary orbits in the Copernican theory. Mathematical details are also provided for Kepler’s Laws of Planetary Motion, Galileo’s measurement of mountains on the Moon, Galileo’s studies of falling bodies and projectiles, Newton’s universal gravitational force, and Bradley’s theory of the aberration of starlight.

Although Newtonian physics provided a sensible explanation for why the Earth should rotate on its axis and orbit the Sun, there was still no direct evidence for Earth’s motion. The first such evidence was provided by James Bradley, who attempted to reproduce Hooke’s parallax measurements and instead discovered the aberration of starlight. This slight displacement of a star’s apparent position occurs because of the Earth’s orbital motion and the finite speed of light. It was not until the late 1830s that astronomers finally detected annual stellar parallax, again confirming Earth’s orbital motion. Astronomers also sought direct evidence for Earth’s rotation. French astronomers confirmed that the Earth bulges out slightly at the equator, an effect that Newton had predicted as a result of Earth’s rotation. Experiments on the deflection of falling bodies also seemed to confirm Earth’s rotation, but the results were clouded in uncertainty. It was Foucault’s famous pendulum that provided the best direct evidence for the rotation of the Earth. These and other successes helped to establish the validity of Newtonian physics and brought about the successful conclusion of the Copernican Revolution.