Work with AD Groups

Get all groups a member is part of

Get-ADPrincipalGroupMembership -Identity "Username"

Export a Report of All the Groups with their Members

This will export one text file with each group name and the members under it

$Groups = Get-ADGroup -Properties * -Filter * -SearchBase (Get-ADDomain).DistinguishedName
Foreach($Group In $Groups) {
    "-------------" | Out-File -Append -filepath 'Groups.txt'
    $Group.Name | Out-File -Append -filepath 'Groups.txt'
    "-------------" | Out-File -Append -filepath 'Groups.txt'
    Get-ADGroupMembers -Identity $Group | Select Name,objectClass | Out-File -Append -filepath 'Groups.txt'
    "`n" | Out-File -Append -filepath 'Groups.txt'
}

This will export one CSV for each group, with the members of that group

$Groups = Get-ADGroup -Properties * -Filter * -SearchBase (Get-ADDomain).DistinguishedName
Foreach($Group In $Groups) {
    $name = $Group.Name
    Get-ADGroupMembers -Identity $Group | Export-csv C:\Temp\Client\$name.csv
}