All the Premier League transfers of the big six in this summer window

Arsenal
IN:
Stephan Lichtsteiner (Juventus)
Bernd Leno (Bayer Leverkusen)
Sokratis Papastathopoulos (Dortmund)
Lucas Torreira (Sampdoria)
Matteo Guendouzi (Lorient)

OUT:
Per Mertesacker (retired)
Santi Cazorla (released)
Takuma Asano (Hannover) Loan
Jack Wilshere (West Ham)
Vlad Dragomir (released)
Ryan Huddart (released)
Tafari Moore (released)
Hugo Keto (Brighton)
Chiori Johnson (released)
Yassin Fortune (released)
Aaron Eyoma (released)
Alex Crean (released)
Marc Bola (released)
Kelechi Nwakali (FC Porto) Loan
Jeff Reine-Adelaide (Angers)
Matt Macey (Plymouth) Loan
Chuba Akpom (PAOK Salonika)
Joao Virginia (Everton)
Calum Chambers (Fulham) Loan
Lucas Perez (West Ham)

It seems that Arsenal strengthen their squad in this summer window bringing in quality players like Sokratis and Leno. They also got a new coach, Unai Emery.

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Chelsea
IN:
Jorginho (Napoli)
Robert Green
Mateo Kovacic (Real Madrid)
Kepa Arrizabalaga (Athletic Bilbao)

OUT:
Mitchell Beeney
Wallace Oliveira
Trevoh Chalobah (Ipswich) Loan
Nathan Baxter (Yeovil) Loan
Reece James (Wigan) Loan
Dujon Sterling (Coventry) Loan
Lewis Baker (Leeds) Loan
Jake Clarke-Salter (Vitesse) Loan
Danilo Pantic (Partizan) Loan
Jonathan Panzo (Monaco)
Eduardo (Vitesse) Loan
Kenedy (Newcastle) Loan
Jhoao Rodriguez (Tenerife) Loan
Jamal Blackman (Leeds) Loan
Todd Kane (Hull) Loan
Mason Mount (Derby) Loan
Jeremie Boga (Sassuolo)
Mario Pasalic (Atalanta) Loan
Nathan (Atletico Mineiro) Loan
Jacob Maddox (Cheltenham Town) Loan
Victorien Angban (Metz) Loan
Kasey Palmer (Blackburn) Loan
Kyle Scott (Telstar) Loan
Thibaut Courtois (Real Madrid)
Michy Batshuayi (Valencia) Loan
Kurt Zouma (Everton) Loan
Tiemoue Bakayoko (AC Milan) Loan

Chelsea had an ok window with the new manager Maurizio Sarri seeing his first choise goalkeeper Thibaus Courtois leave the club. Chelsea brought Kepa Arrizabalaga as his replacement from Athletic Bilbao on a deadline deal and a record-breaking 80million transfer fee.

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Liverpool:
IN:
Fabinho (Monaco)
Naby Keita (RB Leipzig)
Xherdan Shaqiri (Stoke City)
Alisson Becker (AS Roma)

OUT:
Yan Dhanda (Swansea)
Ovie Ejaria (Rangers) Loan
Emre Can (Juventus)
Jon Flanagan (released)
Adam Bogdan (Hibernian) Loan
Harry Wilson (Derby) Loan
Paulo Alves (Wolves)
Danny Ward (Leicester)
Andy Firth (Barrow)
Ryan Kent (Rangers) Loan
Taiwo Awoniyi (Gent) Loan
Shamal George (Tranmere) Loan
Allan (Frankfurt) Loan
Ben Woodburn (Sheffield United) Loan
Danny Ings (Southampton) Loan

Liverpool brought in Alisson Becker from Roma and managed to not let any of the club's big players to leave.

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Manchester City
IN:
Riyad Mahrez (Leicester)
Claudio Gomes (PSG)
Philippe Sandler (PEC Zwolle)
Daniel Arzani (Melbourne City)

OUT:
Pablo Maffeo (Stuttgart)
Yaya Toure (released)
Angelino (PSV)
Ashley Smith-Brown (Plymouth)
Matt Smith (Twente) Loan
Edward Francis (Almere City) Loan
Manu Garcia Alonso (Toulouse) Loan
Angus Gunn (Southampton)
Paolo Fernandes (NAC Breda) Loan
Jack Harrison (Leeds United) Loan
Aro Muric (NAC Breda) Loan
Bersant Celina (Swansea City)
Aleix Garcia (Girona) Loan
Tosin Adarabioyo (West Brom) Loan
Joe Hart (Burnley)
Thomas Agyepong (Hibernian) Loan
Lukas Nmecha (Preston North End) Loan

City had a really quiet window singing only Mahrez from Leicester. City also kept all the first team players.

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Manchester United
IN:
Diogo Dalot (Porto)
Fred (Shakhtar)
Lee Grant (Stoke)

OUT:
Michael Carrick (retired)
Joe Riley (Bradford)
Dean Henderson (Sheff Utd) Loan
Sam Johnstone (West Brom)
Daley Blind (Ajax) Undisclosed
Matty Willock (St Mirren) Loan
Cameron Borthwick-Jackson (Scunthorpe) Loan
Joel Pereira (Vitoria Setubal) Loan
Axel Tuanzebe (Aston Villa) Loan
Timothy Fosu-Mensah (Fulham) Loan
James Wilson (Aberdeen) Loan

Manchester United had a very dissapointed transfer window. They brought in Fred, Dalot and Grant. Also, club legend Michael Carrick retired.

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Tottenham
IN:

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OUT:
Keanan Bennetts (Borussia Monchengladbach)
Anton Walkes (Portsmouth)

Tottenham had the most silent transfer window ever. The Tottenham board made no signing, while on the other hand managing to keep all the key players including Harry Kane, who signed a contract extension.