Reference for the Construction of Brownian Motion

The monograph Brownian Motion - An Introduction to Stochastic Processes by René Schilling & Lothar Partzsch contains (proofs of) the following constructions of Brownian motion:

• Lévy-Cieselski construction
• Wiener's construction
• Lévy's construction
• construction via orthogonal series
• (sketch of) Donsker's construction
• construction via Kolmogorov's existence theorem