Toggle-buttons - Exclusive selection - https://material.io/guidelines/components/buttons.html#buttons-toggle-buttons

demo.js

import { RadioButton, RadioButtonGroup } from 'material-ui/RadioButton';
import RaisedButton from 'material-ui/RaisedButton';
import ToggleButtonGroup from './ToggleButtonGroup'
...

<ToggleButtonGroup>
  <RaisedButton 
    label="Beginner"
    style={styles.customStyle}
  />
  <RaisedButton
    label="Intermediate"
    labelPosition="before"        
    style={styles.anotherCustomStyle}
  />
  <RaisedButton
    href=""
    target="_blank"
    label="Expert"
    style={styles.button}
    icon={""}
  />
</ToggleButtonGroup>

ToggleButtonGroup.js

// compatible with http://www.material-ui.com

// the radius style can be change at each button lvl 
// please mention the original Gist if you find this useful, Thank you :)

const ToggledGroupStyles = {
  radius: 4,
  button: {
    left: {
      borderRadius: '4px 0px 0px 4px'
    },
    middle: {
      borderRadius: 0
    },
    right: {
      borderRadius: '0px 4px 4px 0px'
    }
  }
}

export default class ToggleButtonGroup  extends Component {
  onToggleButtonClick(idx, e) {
    this.setState({ selectedIndex: idx })
  }
  constructor(props) {
    super(props)
    this.state = {
      selectedIndex: this.props.selectedIndex || 1,
    }
    this.styles = ToggledGroupStyles
    this.buttonType = this.props.buttonType || "primary"
  }
  

  render() {
    let { children } = this.props
    const newChildren = children.map((child, idx) => {
      // select the right style depending on child position
      let buttonStyle = (![0, children.length - 1].includes(idx)) ?
          this.styles.button.middle : idx == 0 ? this.styles.button.left : this.styles.button.right
      return React.cloneElement(child, {
          key: idx,
          primary: ((this.state.selectedIndex === idx) &&(this.buttonType=="primary") ? true : false),
          secondary: ((this.state.selectedIndex === idx) &&(this.buttonType=="secondary") ? true : false),
          buttonStyle: Object.assign({}, buttonStyle, child.buttonStyle),
          style: Object.assign({}, buttonStyle, child.style),
          onClick : this.onToggleButtonClick.bind(this, idx )
      })
    })
    return (
      <div>
      {newChildren}
      </div>
    )   
  }          
}

Demo 1