Learn Russian: Масштабная интеграция рынков начнётся завтра. - The large-scale integration of the markets will begin tomorrow.

In Russian, verbs for starting and finishing (начать/начаться, закончить/закончиться) have two forms. If a subject is starting a separate object (transitive), you use начнёт. Because the integration is starting on its own (intransitive), we need the reflexive form with the -ся ending: начнётся.

Why is the genitive plural of рынок written as рынков without the о?

The noun рынок (market) contains a fleeting vowel. The last о in the root drops out when you add case endings. So to form the genitive plural, the о falls out, giving us the stem рынк-, to which we add the standard masculine -ов ending to make рынков.

Since this lesson covers в ходе (in the course of), how would I say 'in the course of the integration' using this sentence's vocabulary?

To say 'in the course of the large-scale integration', you would use в ходе followed by the genitive case: в ходе масштабной интеграции. Notice that feminine nouns ending in -ия like интеграция take an -ии ending in the genitive, rather than the usual -ы or -и.

What is the root of масштабная and how else is it used?