Here's a list of important planetary movements and alignments for this month:

Movements and Aspects:
2nd Mercury enters Cancer, Mars enters Leo, Sun square Moon (First Quarter)
4th Moon's apogee (furthest from the Earth)
11th Sun opposition Moon (Full Moon)
12th Moon's maximum southern declination
16th Moon's perigee (closest to the Earth)
17th Saturn quintile Uranus - exact on this day
18th Sun square Moon (Last quarter)
19th Uranus stations and turns retrograde
20th Saturn opposition Chiron
21st Sun enters Cancer (Solstice - Summer in Northern hemisphere, Winter in Southern hemisphere)
22nd Moon's north node enters Pisces, Jupier square Saturn - exact on this day
24th Venus enters Gemini
25th Sun conjunct Moon (New Moon), Moon's maximum northern declination
28th Mercury enters Leo
30th Saturn sesquiquadrate Pluto - exact on this day

Aspect formations:
From 5th to 8th there is a Grand Cross aspect formation between Venus, Jupiter, Saturn, and Chiron
From 4th June to 9th July there are various T-Square aspect formations between Sun, Venus, Mars, Jupiter, Saturn, and Chiron