Serena Williams has claimed 23 grand slams during an illustrious career but the American superstar ranked Tuesday's Australian Open first-round rout of Tatjana Maria as the "greatest win of my career".

Former world number one and this year's 16th seed Williams flexed her muscles in a 6-0 6-2 demolition of German Maria at Melbourne Park.

Williams was back in Melbourne for the first time since winning the 2017 Australian Open - the 37-year-old skipping last year's event following the birth of her daughter.

And veteran Williams, who is seeking an eighth Australian Open title, revelled in the result afterwards.

"I think the last time I was here I was actually pregnant and playing at the same time," Williams said in her on-court interview.

"It was weird walking out here on my own this time. It is great to be back. That was literally the greatest win of my career."

Williams produced a merciless performance on Rod Laver Arena, sailing through to the second round in just 49 minutes.

She completely overpowered Maria, highlighted by a devastating 18-minute opening set, which yielded nine winners.

Williams also tallied 24 points compared to Maria's five, before her beleaguered opponent managed to snare two games in the second set.

In her post-match news conference, Williams – who refused to comment on last year's infamous meltdown in the US Open final – told reporters: "I didn't make too many unforced errors.

"She's a tricky player. Could have been easily a 6-3, 6-4 match or three-set match. She's been able to beat top players, number one and two, so she knows how to play. I think always when I have a tougher round or I know someone that's really good, I really want to be focused, and then that was really helpful for me today."

Williams unveiled a new eye-catching green bodysuit in Melbourne, where she was also wearing compression stockings.

Asked if she was still worried about the thrombosis issue revealed in 2011, Williams said: "Definitely still concerned. I have had some issues, and they're not done. So, it's just something I just have to do for pretty much probably the rest of my career, we'll see. But I'm always at the doctor.

"With DVTs, it's very scary. I know a lot of people – they're very common. A lot of people have them. Especially for me it's incredibly frightening. I lay on the side of precaution as opposed to not."