  We present a sample of $\sim 1000$ emission line galaxies at $z=0.4-4.7$ from
the $\sim0.7$deg$^2$ High-$z$ Emission Line Survey (HiZELS) in the Bo\"otes
field identified with a suite of six narrow-band filters at $\approx 0.4-2.1$
$\mu$m. These galaxies have been selected on their Ly$\alpha$ (73), {\sc [Oii]}
(285), H$\beta$/{\sc [Oiii]} (387) or H$\alpha$ (362) emission-line, and have
been classified with optical to near-infrared colours. A subsample of 98
sources have reliable redshifts from multiple narrow-band (e.g. [O{\sc
ii}]-H$\alpha$) detections and/or spectroscopy. In this survey paper, we
present the observations, selection and catalogs of emitters. We measure number
densities of Ly$\alpha$, [O{\sc ii}], H$\beta$/{\sc [Oiii]} and H$\alpha$ and
confirm strong luminosity evolution in star-forming galaxies from $z\sim0.4$ to
$\sim 5$, in agreement with previous results. To demonstrate the usefulness of
dual-line emitters, we use the sample of dual [O{\sc ii}]-H$\alpha$ emitters to
measure the observed [O{\sc ii}]/H$\alpha$ ratio at $z=1.47$. The observed
[O{\sc ii}]/H$\alpha$ ratio increases significantly from 0.40$\pm0.01$ at
$z=0.1$ to 0.52$\pm0.05$ at $z=1.47$, which we attribute to either decreasing
dust attenuation with redshift, or due to a bias in the (typically)
fiber-measurements in the local Universe which only measure the central kpc
regions. At the bright end, we find that both the H$\alpha$ and Ly$\alpha$
number densities at $z\approx2.2$ deviate significantly from a Schechter form,
following a power-law. We show that this is driven entirely by an increasing
X-ray/AGN fraction with line-luminosity, which reaches $\approx 100$ \% at
line-luminosities $L\gtrsim3\times10^{44}$ erg s$^{-1}$.
