  In the series of lectures, we will discuss probability laws of random points,
curves, and surfaces. Starting from a brief review of the notion of
martingales, one-dimensional Brownian motion (BM), and the $D$-dimensional
Bessel processes, BES$_{D}$, $D \geq 1$, first we study Dyson's Brownian motion
model with parameter $\beta >0$, DYS$_{\beta}$, which is regarded as
multivariate extensions of BES$_D$ with the relation $\beta=D-1$. Next, using
the reproducing kernels of Hilbert function spaces, the Gaussian analytic
functions (GAFs) are defined on a unit disk and an annulus. As zeros of the
GAFs, determinantal point processes and permanental-determinantal point
processes are obtained. Then, the Schramm--Loewner evolution with parameter
$\kappa >0$, SLE$_{\kappa}$, is introduced, which is driven by a BM on
${\mathbb{R}}$ and generates a family of conformally invariant probability laws
of random curves on the upper half complex plane ${\mathbb{H}}$. We regard
SLE$_{\kappa}$ as a complexification of BES$_D$ with the relation
$\kappa=4/(D-1)$. The last topic of lectures is the construction of the
multiple SLE$_{\kappa}$, which is driven by the $N$-particle process on
${\mathbb{R}}$ and generates $N$ interacting random curves in ${\mathbb{H}}$.
We prove that the multiple SLE/GFF coupling is established, if and only if the
driving $N$-particle process on ${\mathbb{R}}$ is identified with DYS$_{\beta}$
with the relation $\beta=8/\kappa$.
