Atletico Madrid, Spain La Liga titleholders

Previous season winner, title defender, Atletico Madrid is prised as the third favourite after Real Madrid and Barcelona to win the Spain La Liga.
The only notable departure is Lucas Torreira, who went back to Arsenal after playing as a loanee in Spain for one season. 
They did strengthen the squad with two decent signings. Argentina midfielder Rodrigo de Paul came from Udinese with a price tag of 31m. The attack-minded midfielder with 9 goals in last season in Serie A in his best years is for sure a decent signing during this summer transfer window, especially when comparing other competitors transfer windows.

A few days ago, they confirmed the signing of Matheus Cunha. The Brazilian-born striker joined them from Hertha for 27m. 7 goals last season and is only 22 years old, so he should be Luis Suarez's replacement soon.
Spain La Liga title defender has won their first two games, both with one goal margin. All three goals were scored by the same man, Angel Correa.
There's a lot of talking about Kieran Trippier returning to England Premier League. With or without him, Atletico will be the title contender this season for sure. Joao Felix and Felipe haven't recovered from the injury yet, and they will be important first team players once they are back. Real and Barcelona are weaker than last season for sure, so it's a perfect scenario going on for Atletico to defend the title.

FC Barcelona

FC Barcelona finished in 3rd place last season, 2nd favourite for this year.
They lost Junior Firpo, left-back with 7 games and 1 goal and youngster Trincao with 28 games and 3 goals to Wolves.
If this had ended here, Barcelona would be in a good place still, but. We witnessed the end of an era during this summer transfer window.
A season ago, Spain La Liga lost Ronaldo. This year, they also lost Lionel Messi. Messi has been an integral, talismanic player for Barcelona since 2004! During his last ten seasons, he scored at least 25 goals per season and 30 goals during the previous season. The saga, which started already before the previous season, finally finished, and Messi joined PSG. Even more, to rub it in, he left as a free transfer due to Barcelona's financial situation. A huge loss for the team and league in general for sure.
Did they recover? It's basically impossible to recover from losing Messi, but they tried to take the maximum out of the tough financial situation.
Considering this, they did a good job.

Barcelona paid 8m in total for 4 players whose market value is around 80m. They started by raiding Manchester City: Sergio Aguero and Eric Garcia came in for free. Aguero's best years are behind him by now, but keep in mind that he joined Barcelona to play with Messi. So now there are big rumours that he wants to leave also, to PSG? Garcia is a young Spanish centre-back and with a great future ahead of him for sure. The great Gerard Pique will mentor him before he hangs his boots.
The defence got some reinforcements with Emerson, who joined from Real Betis for 8m. A top 5 right-back in the league for sure while being still only 22 years old. The most important player who joined Barcelona is Memphis Depay. Came from Lyon for free with a market value of around 40m. Had a 20 goals season in France, and as in the Netherlands national team, he will also be the primary goal threat for Barcelona.

Barcelona has 4 points from the first two games, 5-3 goal difference, and the rebuild. Top 3 in Spain La Liga with a hope to win the league is, of course, there. In the Champions League? They would need a small miracle to beat the teams like PSG, Chelsea or Manchester City on the way.

Real Madrid

Real Madrid finished in the 2nd spot last season, 2 points behind Athletico Madrid and 5 points ahead of Barcelona. The biggest favourite to win the league this season and around 5th to 7th favourite to win the Champions League. It was probably the first transfer window for Real Madrid in the last decade where they made a profit, but mainly because they didn't invest in renewing the squad. 2nd place last season, and at first sight, no need to invest heavily..but but.
We saw another end of an era. For almost a decade, Sergio Ramos and Raphael Varane have been the main central defender pair for the Spain La Liga giants. During this summer, both left the club and Ramos for free.
Long time captain Ramos joined PSG for free, to play together with Lionel Messi? Raphael Varane joined Manchester United to get some new challenges. Manu paid 36m for one of the best central defenders currently playing. A huge loss for Real to lose both their prominent defenders during the same window. Martin Odegaard was sold to Arsenal for 30m and never got a chance to show his skills to Madrid fans. Kubo and Brahim Diaz were loaned out with Alvaro Oriozola.

Striker Luka Jovic and winger Gareth Bale, defender Jesus Vallejo and midfielder Dani Ceballos returned from loans and were kept in Madrid.
The most important addition for sure was defender/midfielder David Alaba who joined Real Madrid for free from Bayern Munich. A strong cover for either of the defenders who left and will be paired with Eder Militao who will now get his chance to play as the starter during the whole season.
Overall, Madrid addressed the weakest areas since the important departures, and Eder is not a pushover. What they need for success is Hazard and Bale raising their game to their previous level when they were the real threats and some of the youngsters to step up, like Vinicius and Rodrygo. 

In their first 2 games, Real scored 7 goals and conceded 4. The goal-scoring luckily haven't been an issue, but the defence has. A lot of missings still as Dani Carvajal, Mendy, and Marcelo haven't featured yet. Two of them should be the starters during the season once fit. Vinicius has shown some great potential once again and is a step-up from last season. Three goals already in 2 games and will be interesting to see how other youngsters respond. For the Spain La Liga title, they will compete until the end with the new coach. To go for the Champions League, I doubt there's enough firepower to beat teams like Chelsea, Manchester City, and PSG.