  In this series of lectures, I review our observational understanding of
high-$z$ Ly$\alpha$ emitters (LAEs) and relevant scientific topics. Since the
discovery of LAEs in the late 1990s, more than ten (one) thousand(s) of LAEs
have been identified photometrically (spectroscopically) at $z\sim 0$ to $z\sim
10$. These large samples of LAEs are useful to address two major astrophysical
issues, galaxy formation and cosmic reionization. Statistical studies have
revealed the general picture of LAEs' physical properties: young stellar
populations, remarkable luminosity function evolutions, compact morphologies,
highly ionized inter-stellar media (ISM) with low metal/dust contents, low
masses of dark-matter halos. Typical LAEs represent low-mass high-$z$ galaxies,
high-$z$ analogs of dwarf galaxies, some of which are thought to be candidates
of population III galaxies. These observational studies have also pinpointed
rare bright Ly$\alpha$ sources extended over $\sim 10-100$ kpc, dubbed
Ly$\alpha$ blobs, whose physical origins are under debate. LAEs are used as
probes of cosmic reionization history through the Ly$\alpha$ damping wing
absorption given by the neutral hydrogen of the inter-galactic medium (IGM),
which complement the cosmic microwave background radiation and 21cm
observations. The low-mass and highly-ionized population of LAEs can be major
sources of cosmic reionization. The budget of ionizing photons for cosmic
reionization has been constrained, although there remain large observational
uncertainties in the parameters. Beyond galaxy formation and cosmic
reionization, several new usages of LAEs for science frontiers have been
suggested such as the distribution of {\sc Hi} gas in the circum-galactic
medium and filaments of large-scale structures. On-going programs and future
telescope projects, such as JWST, ELTs, and SKA, will push the horizons of the
science frontiers.
